The Lesser Antilles reach south across the Caribbean in a fat arc like steppingstones, stretching from Puerto Rico almost to South America. Wouldn't it be fun to island-hop down this inviting tropical avenue, using only ferries and other local seagoing craft? It is a cruise in which you design the itinerary and travel at your own pace.

Is it possible? Part of the way it is, although major gaps do exist in the long marine route. You almost certainly would have to do some flying between islands, unless you managed to hitchhike on a passing yacht, fishing boat, schooner or freighter. The trip wouldn't be easy or comfortable, but few real adventures are.

It's an ideal voyage for independent travelers in quest of the old romance of the sea -- the sort of people who may disdain the dressed-up glitter of luxury cruise ships but who don't have a seafarer's knowledge to sail their own boat or the money to charter one.

Though it is little advertised, many of the islands of the southern Caribbean are linked by regular passenger boat service. In style, the craft vary from sleek new power boats catering mostly to tourists to sturdy old inter-island mail boats carrying local islanders, an occasional tourist and food supplies and other cargo. Cruise ships don't count, because you can't get off and on where and when you choose.

The old ferries, says Marcella Martinez of the Caribbean Tourism Organization, "are a slice of island life. You may find yourself sitting beside a generator headed for a hotel or a lady with a pig in her lap." Before the advent of air travel, all commerce between Caribbean islands had to be by boat. "The ferries are what the islanders use."

"If we have corn planted in Bequia," says Helen Ollivierre Williams of the St. Vincent and the Grenadines Tourist Office, "relatives from Canouan come up on the boat to help reap for two or three days. That's how we do it in the Grenadines."

The Lesser Antilles extend perhaps 700 miles from San Juan to St. George's in Grenada, and between them lie more than two dozen possible ports of call. To travel the full length by sea wherever possible might take weeks, which restricts such a trip to free spirits with time to spare. Still, the dream is not an impossible one, especially as inter-island boat service grows.

Travelers with strictly limited time who want to explore the Caribbean by scheduled passenger vessel can do so readily in neighboring clusters of islands. Any of the island trips will give you plenty of sea time to breathe in the salt air. Good ferry service, for example, connects several of the British Virgin Islands with St. Thomas and St. John in the U.S. Virgins. In addition:

The dual French and Dutch island of St. Martin/Sint Maarten is a hub for inter-island sea traffic with links to Anguilla, St. Barts and Saba.

Twice-weekly ferries out of St. Vincent call on Bequia, Canouan and other small islands in the lovely Grenadines chain.

Some 20 mail boats carrying passengers and cargo depart weekly from Nassau to the Bahamian out islands.

A large new high-speed ferry, the 227-passenger Blue Manta, has begun serving the French islands of Guadeloupe and Martinique, connecting them by water to neighboring Dominica and St. Lucia. In 1991, this Martinique-based company, Caribbean Express, expects to add a second ferry. It will then be possible, says the company, to extend service north to Antigua, St. Barts and St. Martin and south to St. Vincent.

A local ferry currently runs between St. Kitts and Nevis, and a new high-speed ferry, the Spirit of Mount Nevis, will be launched later this month. It will cater to the tourist market.

The eastern Puerto Rican port of Fajardo is the departure point for ferries to the offshore islands of Culebra and Vieques.

Just off the coast of South America, auto ferries link the islands of Trinidad and Tobago.

As inviting as such travel may sound -- at least to vagabond souls -- there are drawbacks and inconveniences.

So far, no single publication contains a complete list of Caribbean island ferry and boat schedules. To plan an itinerary, however, you can obtain reasonably accurate schedule information by contacting each island's tourism office -- either in New York or in the island's capital city. Officials can tell you what sea links (or air, if necessary) their island has with its neighbors. With this information, you can piece together an itinerary island by island.

At least two annual Caribbean guidebooks make brief mention of each island's sea links on an island-by-island basis. "Caribbean Island Handbook," edited by Ben Box and Sarah Cameron (Prentice Hall, $15.95), seems the most informative. But "Fielding's Caribbean" by Margaret Zellers (Fielding, $13.95) is almost as good. Neither really pays the subject the attention it deserves, however, at a time when vacationers increasingly are looking for offbeat and authentic adventures.

Ferry boat schedules, say tourism officials, can be erratic -- depending, among many things, on the day's weather, how rough the seas are and how long it takes to load and properly secure the cargo. Some ferries sail overnight, and you might have to spend the night napping on the deck under the stars. (In the warm tropics, this is not as arduous as it may sound.) Seasickness is a possibility.

Fares vary wildly. Government ferries tend to be inexpensive; passage on the tourist-oriented, high-speed power boats comes close to equaling the cost of an airline ticket over the same distance.

If you are planning a trip:

Travel light. A small backpack with a couple of changes of warm weather clothing should be plenty.

Book rooms ahead. Some of the smaller Caribbean islands have very limited tourist accommodations. Make advance reservations so you know you have a room when you arrive. The next ferry may not show up for several days.

Relax. In the Caribbean, schedules are flexible, and you will have to adapt.

The following island-hopping information is compiled from Caribbean tourism offices. But sailing schedules change with the seasons, and new service is added or abandoned with some frequency. Some officials point out that these itineraries reflect only a small portion of the inter-island boat traffic. Once you are on an island, you may learn of fishing boats, cargo schooners or other vessels on which you may buy passage onward.

17-island grand tour: Using currently published schedules, travelers should be able to island-hop more than half the length of the Lesser Antilles. One flight en route is almost a certainty, at least until 1991.

You begin the trip at Guadeloupe, boarding the Caribbean Express's Blue Manta. The Blue Manta will carry you south, in turn, to Dominica, Martinique and St. Lucia. From St. Lucia, you will have to make a short flight to St. Vincent. Both the St. Lucia and St. Vincent tourism offices say there is no scheduled sea link between their islands. LIAT, the Caribbean airline, offers several daily flights.

From Kingstown, the capital of St. Vincent, the MV Snapper, a large ferry, makes a twice-weekly (Monday and Thursday) run down the St. Vincent Grenadines, calling at Bequia, Canouan, Mayreau and Union Island -- all inviting stops. From Union Island, daily ferry service is available to Carriacou, an island that is a part of the nation of Grenada. From Carriacou, take another daily ferry to Grenada, the end of the line.

A 12-hour passage on cargo freighters sailing between Grenada and Trinidad is a possibility that could extend your itinerary, according to two Caribbean tourism spokeswomen, but this could not be confirmed.

Out of Guadeloupe, side trips by boat can be made to the French islands of Marie Galante, Desirade and Les Saintes. Out of St. Vincent, it is possible to take a Sunday sea excursion to exclusive Mustique. Out of Union Island, side trips to the resort islands of Palm Island and Petit St. Vincent are possible. On this itinerary, the number of islands visited comes to at least 17.

If Caribbean Express adds a second ferry to its service in 1991, as planned, travelers could begin their island hop in St. Martin and stop also at St. Barts and Antigua. The new schedule would also include service between St. Lucia and St. Vincent, so no flight would be necessary. For seagoers, it is an inviting prospect.

Caribbean Express's Blue Manta is a two-deck catamaran with space enough to provide such first-class amenities as audio-equipped reclining seats, snack bar, lounge and duty-free shop. The vessel began island hopping on June 30, and so far has carried more than 22,000 passengers, according to commercial manager Roland Bellemare.

The "winter" schedule from now through June 24 calls for sailings from Guadeloupe to Dominica and Martinique on Tuesday, Friday, Saturday and Sunday. On Wednesday, there is a departure from Martinique for St. Lucia. All times at sea are less than two hours.

Each of the three legs of the trip is $44 one way for adults. A 10 percent discount is offered to students under 26 and seniors 60 and older. For information: Caribbean Express, Immeuble O.G.M., Avenue Maurice Bishop 97200, Fort-de-France, Martinique, French West Indies. Phone: (011) 596-60-12-38.

The Bahamas: A fleet of 20 government mail boats sails weekly from Nassau to many of the 700 islands of the Bahamas. Passage is slow, but you will get a more authentic look at Bahamian life than do most tourists. For information: In Nassau, the Mail Boat Dock Master, (809) 323-1064.

Puerto Rico: Daily ferry service is available between Fajardo on Puerto Rico's east coast and the islands of Vieques and Culebra. Very soon, ferry service between Culebra and Vieques also is expected to resume; it was temporarily halted by damage from Hurricane Hugo. This will again make it possible to travel by ferry in a circle route from Fajardo to Vieques to Culebra and back to Fajardo. Travel time between Fajardo and Culebra is 75 minutes, and the one-way fare is $2.25.

Virgin Islands: In the U.S. Virgins, frequent 20-minute ferries link Red Hook on the east end of St. Thomas with St. John. The one-way fare is $2. Ferries sail daily from both St. Thomas and St. John to Tortola in the British Virgin Islands. From Tortola, other ferries continue on to Virgin Gorda, Jost Van Dyke and Peter Island in the British Virgin Islands.

St. Martin and its neighbors: Making St. Martin or Sint Maarten a base point, travelers can find diverse boat service to Anguilla, St. Barts and Saba.

Inexpensive ferries run between Anguilla and St. Martin about every 40 minutes into the evening. To St. Barts, you can take passage on an excursion catamaran leaving Dutch Sint Maarten every morning. Sailing time is about 90 minutes, and the one-way fare is $25. The St. Barts Express, a 12-passenger open motorboat, makes the trip Monday, Wednesday and Friday. The one-way fare is about $27.

To Saba, you can travel as a one-way passenger on Style, an excursion "party" boat, which offers an open bar with the price of passage. "We all use it as a ferry," says Joan Medhurst, a spokeswoman for the island of Saba. "It's a fun thing to do." The Style departs St. Martin about 9 a.m. for Saba, returning at 5 p.m. The round-trip fare is $45.

St. Kitts and Nevis: The 150-passenger Caribe Queen is the traditional ferry between the two islands. It makes the trip daily in 45 minutes. The one-way fare is $4. Beginning about Feb. 15, the high-speed Spirit of Mount Nevis will inaugurate inter-island trips, promising tourists more comfortable seating and cutting the travel time to 30 minutes. The one-way fare will be $6.

The Grenadines: The ferry Snapper, which sails the Grenadines out of St. Vincent, carries about 200 passengers. It departs Kingstown at 10:30 a.m. on Monday and Thursday headed south and reaches Union Island at the end of the chain at 3:35 p.m. -- stopping en route at Bequia, Canouan and Mayreau. (The return trip north is Tuesday and Friday.) The total fare one-way is about $25. For information: Saint Vincent and the Grenadines Tourist Office, 801 Second Ave., 21st Floor, New York, N.Y. 10017, (212) 687-4981.

Trinidad and Tobago: A single nation, the two islands are linked by daily auto-ferry service. The one-way trip takes about six hours.