MY PARENTS went to Europe in 1976 and had a perfectly awful time, which they still laugh about--now.

In Italy they passed up reserved seating to catch an earlier train to Rome and wound up standing or sitting on the floor nine hours. In Rome, my father had his wallet stolen. Later, in Florence, they boarded a train for Venice and discovered too late they were trapped on a "rapido" express back to the Eternal City--where officials charged them for the ride. In Paris, my father lingered so long at the airport employes' cafeteria, the first cheap eating spot he'd found in that city, that they missed their flight to London.

And in London, where I met them, our evening boat ride on the Thames ended abruptly when the tour operator spotted a man's body in the water and my father--after handing my mother his new wallet--helped hoist it aboard.

People couldn't believe so many things could go wrong on one trip. They're not going to believe me, either.

Some "highlights" of my recent trip to Europe:

* The rental car broke down in Ireland. Twice. Searched, luggage in tow, for a hotel room in Paris until nearly 2 a.m.

* Had my wallet, traveler's checks and glasses stolen in Italy.

* The tickets for my return home from Milan were on a flight that didn't exist and with an airline that didn't service that city.

* Luggage that arrived safely in New York from Italy was lost enroute to Washington.

Let me say right off that I'm an experienced traveler. I've been to Europe half a dozen times, starting with a two-month bicycle tour in 1964, and even visited Vietnam and Cambodia in 1973 to see a friend covering the war. And though last month's problem-plagued trip turned out to be the most stressful vacation of my life, I actually had a nice time anyway. Really.

So go to Europe. I certainly will again. And if you let my experience be your precaution, these horror stories cannot possibly happen to you. (Or at least not all at once . . .)

The car, which we rented just for Ireland, broke down the second day of our vacation. My traveling companion, a woman who never had been to Europe, and I had a pretty tight, three-week schedule, calling for us to start out in Ireland and end up in Italy--with London, Paris, the southern part of France and one or two towns in Switzerland sandwiched in between. We could ill afford travel disruptions.

We were staying with friends in a thatched cottage at Tully Cross, a one-pub town in Ireland's rugged Connemara section, and had just returned from Inishbofin, an island off the western coast, when the car conked out. (In fact, our Inishbofin trip had been cut short when the boat captain was met at the dock by island residents who asked him to return to the mainland because of a family emergency. Obviously an omen of trouble to come.)

By the time we got to the nearest telephone back at the town pub (this is rural Ireland, remember), all the rental car offices were closed. Instead of the planned leisurely drive south, we spent the better part of the next day feeding coins into a hand-cranked telephone and arguing with the car rental office: we wanted to get a new car and get going, they wanted us to wait and get the car fixed.

A mechanic eventually arrived and got the car started again. Then, barely on our way, the gas pedal suddenly stuck. Fortunately, this happened while we were stopped at a village service pump. Unfortunately, we had just purchased $14 worth of gasoline. More hand-cranked calls to the rental firm, which finally dispatched a cab to drive us south to Galway to get another car. But we weren't back on the road until almost 5 p.m., with nearly four hours of driving ahead of us to reach Killarney.

LESSON: Make sure the car rental firm gives you the numbers (including night numbers) of its offices and service garages. Find out in advance what a car rental's emergency procedures are, and make sure you're dealing with a firm that gives you prompt attention and won't balk at getting you a new car if you're pressed for time.

The next travel horror was mostly our own fault. We deliberately avoided making advance hotel or guest house reservations because we didn't want to be tied to a fixed itinerary. That works fine unless you arrive someplace late at night or end up in a city that is especially teeming with tourists. After a terrific stay in London, we arrived in Paris at nearly 10 p.m. and found every budget hotel--those we called and those we happened upon--"complet" (full). Of course, the Paris Air Show, the upcoming French Open and the fact that it was nearly the height of the tourist season might have had something to do with this.

After calling several budget hotels from the train station and finding them full, we took the Metro several stops further out and then walked up and down streets looking for a room. The later it got, the more we attracted the attention of Parisian men, who had plenty of interest in and suggestions for our sleeping arrangements. Finally, after taking a taxi to yet another part of the city, we found one empty room. A "double," the manager said. It turned out to have just a double bed, with a mattress that dipped into a decided "V", but it got us off the streets. I woke up in that room on my birthday, hanging onto the mattress to keep from sliding into the center. Somehow, it wasn't the happy moment I had anticipated.

LESSON: Pay attention to what is taking place in the cities you visit. If it's going to be a particularly touristy time, arrive early so you or the tourist office have time to look for lodging. Even if you only have one bag (which is all you should have if you're moving around a lot), bring a luggage carrier. Also, if you're going to be calling for hotel rooms, make sure you arrive with--or can get--plenty of change in the currency of the country you're visiting. And that you know how to work the phones and exactly what coins you need for local calls. Otherwise, you may drop a small fortune into the phone box. We did--in almost every country we visited.

Feeling put off by the experience the night before, we cut short our stay in Paris, scratched plans to travel in southern France and headed straight for Switzerland, visiting Lucerne and Interlaken, which were lovely. No problems there. The Swiss really love tourists and take care to provide multilingual guidance and even creatively helpful illustrations for travelers.

Italy was another matter. Taking a night train from Interlaken to Venice (so we could arrive there early), we had to change trains twice and heed orders to move forward whenever we got settled in. (Not all the cars go to the same place, and the Italians don't bother to see that you get into the right train section to begin with.)

And then, somewhere between Milan and Venice, somebody came into the compartment where we slept, opened my purse and stole my wallet ($40 in Swiss money, all my credit cards and personal identification), most of my traveler's checks and my glasses. Except for my glasses, which I thought had fallen out of my purse, I didn't realize anything was amiss until I went to change my Swiss francs into Italian lire later that morning. My friend, more cautious than I, had slept on her purse, so nothing of hers was taken. I had mine by my side. At least one other woman on the train was similarly robbed, also losing her passport.

For the next day and a half, I spent my vacation dealing with Italian police, bank officials, the American Express office and the people who run the telephone facilities at Venice's central post office. There were endless forms to fill out, police reports to sign, long distance calls to make..

The good news in all this is that American Express is even better than its advertisements say it is. It had an office right at San Marco square and issued me a new credit card the next day. Also, I had stashed a small amount of backup traveler's checks in my suitcase and still had my passport, so I could cash them.

The bad news (and I realize I have the makings for a television commercial here) is that I did not have American Express traveler's checks. Thus, I had to call California (the only number listed on the check forms) and then London to report the loss and request replacement checks. True, the calls were collect, but I did not enjoy standing in a telephone booth (remember Ireland and Paris?) at the post office and answering questions about my financial background for nearly an hour. I got partial replacement of the checks in two days, but only after filling out a four-page form that demanded to know, among other things, my bank account number, the address of my bank, my employment history and the names and addresses of personal financial references.

I also spent a good deal of time tracking down the necessary phone numbers and reporting the theft of several other credit cards (travel, bank, etc.) that could have been used abroad.

I negotiated all this while wearing my prescription sunglasses, my only means of adequate visibility. I was forced to wear them day and night, even into the darkest of churches, for the remainder of my trip. And yes, I drew stares from others as I peered intently through my shades at the stained glass windows.

LESSON: You can't be too careful. Don't leave your purse unguarded for a minute, even if it means sleeping on it. I may go to Europe next time with a money belt, like the American nun I met. DO split up your valuables. Carry traveler's checks in two separate places. Keep important check numbers in a third place, along with a record of what checks you've cashed so far. DON'T take your regular wallet and everything in it. I may have needed my driver's license for the trip, but I didn't need my Woodies, Choice and Gulf cards, nor my press identification nor my auto registration--all of which I'm in the process of replacing now.

The anguish and hassle of losing my belongings were soon eased by the beauty of Venice, however, and the final few days of my vacation were quite wonderful. Then it was time to go home. We took the train to Milan, where we had tickets to fly home the next day on a major international airline. Since no one answered the airline's phone in Milan when we called, we took a bus to Linate airport to confirm our flight. An airport booking agent--they sell tickets on all flights since airlines do not always have individul representatives at the airports in Italy--told us the flight was a new one and that we could check in the next morning, anytime after 8 a.m. Reassured, we dashed off to see DaVinci's painting of the Last Supper.

We got to the airport well ahead of schedule. By this time we'd had more than our share of travel horrors and really thought the worst was behind us. We were wrong. The airline, it turned out, did not fly in or out of Milan. We were holding Milan-to-New York tickets on a flight that didn't exist..

People like us, airport personnel told us, had been trooping into the Milan airport for the last several days, and we met two similarly stranded travelers at the airport information counter where we all congregated in bewilderment and despair. There we were that Sunday morning: No airline representative at the airport. No airline officials answering the phones at either the Milan or Rome offices, which are closed Sundays. No airport officials showing the least concern about our plight.

One man at the flight booking counter did finally produce the phone number for the airline's check-in counter at the airport in Rome. A call there elicited the by then hardly startling pronouncement that the airline didn't fly out of Milan. No help here, except the suggestion that we come to Rome to fly home.

Airport officials at first told us our tickets were good only on that flight, but as more stranded passengers arrived on the scene, the man at the booking counter began calling other airlines and finally found one that would take our tickets. We could catch its 12:30 p.m. flight but only if we hurried--to Milan's other airport, Malpensa, the city's major international terminal, more than an hour's ride the other side of town! Hurry we did, hailing a taxi, coughing up 70,000 lire (about $50), which fortunately I had, and speeding frantically to the airport.

We made the flight with less than 20 minutes to spare, sacrificing both a calming departure and a long-anticipated trip to the duty-free shop. I don't know how many other passengers on board had suffered through ticket mix-ups, thefts and other indignities during their European tour. I only know that the whole plane broke out in applause when we landed at JFK.

(Note: As I write this, the airline and my travel agent--who shall remain nameless--are still blaming each other for nearly stranding me in Milan. The airline says the Italian government had not given final authority for its New York-Milan route at the time we purchased our tickets. The airline had planned to start the flights June 1 (our tickets were for June 5) but was forced to postpone service another month. A spokesman for the airline says the travel agency should have told me the flight was subject to approval. The travel agency says it did not know that the flight was conditional and that such information was not in the computer it used to book the flight.

The airline says it notified my travel agency on May 18 that it was canceling my flight. I left the country on May 16. The Civil Aeronautics Board says it is not unusual for airlines to sell tickets conditioned upon government approval; what is unusual, it says, is when such flights never get off the ground, so to speak.)

Safe at home, right? Our luggage breezed through customs and we trudged off to make a connecting flight to Washington, for which we had tickets. By this time I was prepared for upheaval. I wasn't prepared, however, to be told that my ticket to Washington was good but my friend's wasn't. Somewhere in the course of our travels, the wrong coupon had been pulled. She still was carrying around the coupon for the Washington-to-Boston flight we had taken on another airline at the start of our trip.

With command of our native English, some fast talking and a little logic, we were able to convince the gate attendants to let us both on the plane. It sat on the runway for an hour, then delivered us safely to Washington. But our luggage, which had crossed the Atlantic that day without any trouble at all, never crossed the luggage carousel at National Airport. I finally got it the next evening.

LESSON: Remember to ask if there is something speculative about your tickets, and only buy them on established routes, not ones that have been "applied for." Reconfirm bookings on international flights a minimum of 72 hours before departure, and check your travel arrangements during the week when you can reach people, not on weekends. Travel with one bag and take it on the plane with you.

I've been home a couple weeks now. I've stood in the long lines at the D.C. Department of Motor Vehicles to get another license and car registration. I've ordered new glasses (two pair). I've written and called all sorts of firms to apply for new credit cards and other identification. I have a new wallet and a new press pass. I have even been reimbursed $200 by the airline for the taxi and the inconvenience suffered while trying to get out of Italy.

I'd like to tell you that the memory of my travel ordeal is fading and that soon I'll laugh about what happened just as my parents do. But as I write this comes a letter from the shop in Venice where I purchased some Murano glassware for myself and as a wedding present for my brother and his wife. Though the sales clerk assured me the price included freight costs and insurance, I now have been told that my purchases are ready for shipment--if only I'll "kindly" send them another $80.60 to cover the cost of packaging and mailing . . .