Have you earned more frequent-flyer miles than you could ever hope to use?

You could decide to give them to friends or relatives to use for free airline trips. Then again, you might prefer to sell the miles for cash. Discount travel brokers currently are offering as much as $1,700 to frequent flyers who have stockpiled 100,000 bonus miles on a single carrier. For 10,000 miles, you might get $50 to $70.

Who wants your extra miles?

Often, it's business travelers looking for bargains on business-class or first-class tickets to Europe or the Orient. This month, United Airlines is charging $4,684 for a round-trip ticket in first class between Washington-Dulles and Frankfurt. But using the mileage credits purchased from you, a discount travel broker might sell a first-class ticket to Frankfurt for only $2,300 -- less than half the airline's price.

An estimated 50 coupon brokers throughout the country buy and sell frequent-flyer mileage and other free travel awards issued by U.S. airlines. Apparently they have found a steady market among seasoned travelers. The airlines, on the other hand, are furious and have gone to court to attempt to quash the trade in mileage awards. Though the carriers have managed to shut down some discount brokers, the market continues to flourish.

Brokers dealing in mileage awards aren't breaking any laws, says Bill Mosley, a spokesman for the Department of Transportation. Nor are the travelers who use their services. The airlines contend, however, that their rules prohibit the sale of bonus miles and other free travel awards, and their policy has been to seize any ticket they discover has been purchased from a broker. They may even expel a traveler caught selling mileage awards from their frequent-traveler programs.

"Don't buy or sell United coupons," reads a United ad appearing in a travel industry publication last month. The ad warns that the tickets will be considered void "and may be confiscated." To counter the threat, reputable discount brokers promise to refund the price of any ticket claimed by an airline.

Brokers say American Airlines has been the most aggressive carrier seeking to detect passengers using broker-traded tickets. Attempts were made to contact an American spokesperson for comment, but repeated calls were not returned.

In fact, relatively few broker-issued tickets are lifted, says Greg Smidt of Travel Exchange, a discount travel broker in Houston. Only one of his customers has lost a ticket in the past six months, and Smidt refunded the money. Smidt is a spokesman for the American Association of Discount Travel Brokers, an organization of 15 brokers formed in 1987 to set ethical standards for its members. Prompt refunds are required by the association's code of ethics.

Mostly it is the brokers themselves who have felt the wrath of the airlines. Smidt says almost all of the large brokers in the business five years ago have been forced to shut down. Most have settled out of court when faced with mounting legal bills. In their place, however, numerous smaller, less-visible broker firms have popped up -- and now there are more than before.

The airlines appear to have targeted the brokers because they don't want to alienate their best customers, the frequent flyers. "The airlines are in a ticklish situation," says Scott Wangsgaard, a lawyer in Salt Lake City who is representing two brokers in cases filed by American Airlines and Delta Air Lines. "It's their best customers who are selling these awards. They are the ones who are flying the most."

I am not recommending for or against use of a coupon broker. Individual travelers must decide for themselves whether they want to violate what the carriers maintain are the rules of their frequent-flyer programs.

The brokers contend that passengers earn the travel awards and ought to be able to dispose of them as they choose. "Thus, many Frequent Flyers elect to transfer and/or sell their awards in violation of what they feel are unjust prohibitions on award redemption," says an informational handbook published by the brokers association. The airlines believe just the opposite -- that they can limit transfers.

Thus far the dispute between airlines and the brokers over the sale of travel awards remains unresolved in the courts, and the underground trade continues.

U.S. airlines began introducing frequent-flyer programs in 1981 to attract business travelers. Many frequent travelers quickly earned tens of thousands of bonus miles, aided by special promotions offering double- and triple-mileage awards for a single flight. Some accumulated more miles than they could readily use.

"The last thing they want to do on their time off is climb into a plane and take another trip," says Smidt. Airlines do permit passengers to give their mileage away, if only to friends and relatives. The discount travel brokers saw yet another alternative. They bought the excess mileage credits, selling them in turn as tickets to other travelers who could make use of them.

Instead of flying away on a holiday, says Smidt, frequent travelers could use the extra money to help pay for their children's college education, fix up their home or buy a boat for their weekend cottage. One seller rescued his home from a bank that was about to foreclose on it because of an unpaid note.

In 1989, several airlines set an expiration date for unused miles, generally three years after they have been earned. Some travelers, realizing they won't be able to take advantage of the free travel before the expiration date, prefer to sell the mileage rather than lose it altogether.

Brokers see themselves as intermediaries, says lawyer Wangsgaard, "matching willing buyers and sellers. They fill a void."

To attract travelers willing to sell mileage, brokers regularly advertise in business travel publications, the Wall Street Journal and USA Today as well as large city newspapers such as The Washington Post. The ads usually can be found in the classified sections under "Tickets" or "Discount Travel."

On average, brokers pay about one cent per mile for bonus miles, says Smidt. They resell the mileage in the form of tickets at a rate of 1.5 to two cents a mile, although the price varies depending in large part on what airline awarded the mileage. The larger airlines -- American, United and Continental -- have a more extensive route system, which makes their bonus miles more valuable.

The free-travel awards of almost all U.S. airlines are traded. An exception is Pan Am, which has made the transfer of its awards in its World Pass program too restrictive to be of any value to most discount brokers. Pan Am's awards can only be used by the traveler who earned them and a companion on the same flight. TWA's awards also are said to be difficult to transfer, so they are not in large demand.

Brokers buy at least three types of free air travel awards:

Frequent-flyer bonus miles. They are the most valuable, because they can be used nationally or internationally for free travel or seating upgrades. Any ticket acquired with frequent-flyer miles is usually good for at least one year.

Denied-boarding or "bumped" coupons. Airlines issue these coupons for a free, round-trip flight to travelers left at the boarding gate when a flight is overbooked. Brokers are willing to take them, but the price is lower than for mileage credits, because most coupons are only good for travel within the United States.

Special awards. Most airlines offer spring and fall bargains to their frequent travelers. If you complete a specified number of round trips, you earn a free ticket as a reward. These, too, are traded by brokers, but again at a lower rate. The drawback to the broker on these awards is that they generally have to be used during a limited time period -- such as between October and mid-December, an off-season for travel.

Individual frequent flyers sometimes sell bonus awards directly to other travelers, eliminating the broker. You also can find their ads in the classified sections of large daily newspapers, including The Washington Post. Selling the awards yourself can be time-consuming, however, especially if you are flooded with phone calls.

Having purchased travel awards, Smidt then sells them in the form of tickets. He specializes in international flights, principally to Europe, the Orient, the South Pacific and South America -- as well as Alaska. Few if any broker tickets are available to Africa and the Middle East, he says. Because U.S. airlines have established partnership arrangements with foreign airlines, Smidt has been able to put clients on most of the major international airlines -- among them Swissair and Singapore Airlines -- and on the supersonic Concorde.

Unlike Smidt, some discount travel brokers, such as Tickets to Go in Cambridge, Md., deal mostly in flights within the United States. And other brokers -- among them Platinum World Travel of Salt Lake City -- handle both domestic and international travel.

Smidt's customers generally are business travelers looking for a bargain on business-class or first-class seats across the Atlantic or Pacific. Typically, he sells tickets for about half the price charged by the carriers. Older travelers looking for the comfort of first-class seating and honeymooners who also want the best seats are among his regular clientele. Leisure travelers on a budget can get better fares by buying an advance-purchase ticket offered by all the international carriers.

Similarly, broker tickets for flights solely within the United States generally are of value only to travelers who must depart on short notice and can't take advantage of the airlines' so-called supersaver fares. If you can plan weeks in advance, for example, you should be able to purchase a supersaver fare to the West Coast for $300 to $400. If you have to fly tomorrow, or you can't stay over a Saturday night, you might have to pay $1,200 or more for the same ticket. Tickets to Go, a small firm catering to the local market, can provide a ticket within a couple of days for $375 to $500, depending on the airline.

Business travelers, however, are not the only travelers who can save money with broker tickets. Family members who have to fly on short notice to a funeral might be able to find a bargain. Some travelers buy "open" tickets that are valid for a year but carry no specific departure date. They keep them on hand for emergencies, such as a family illness or a tentative business meeting. Using an open ticket, these travelers can fly at a moment's notice at no extra fare.

One Houston mother found the open ticket particularly useful, says Smidt. She wanted to join her daughter in Alaska, who was expecting to give birth to twins. But she didn't want to leave home until her daughter's delivery was imminent. With an open ticket, which Smidt sold to her, she was ready to go when the twins announced their arrival -- and at a substantial savings over a standard full fare.

Although legitimate brokers promise a refund if your ticket is confiscated, there are hazards to consider before buying. You must weigh the risk involved in relation to the savings you expect.

If you are at the check-in counter when your ticket is lifted, you probably will have to pay for a full-fare ticket on the spot or cancel your trip. Perhaps even worse, you may have completed the first leg of your trip, but have your ticket seized by the airline as you prepare to return home. To get back, you probably will have to pay for a costly one-way ticket with no option to cancel out.

In such circumstances, brokers are expected to refund only the cost of the ticket they sold you -- and not the added expense incurred in buying a substitute ticket.

Typically, a frequent flyer who wants to sell mileage awards will contact several discount travel brokers to find the best price. Brokers are highly competitive, says Smidt, and rates vary. Each firm has its own procedure for handling the deal, and the process also depends on what airline the mileage was earned.

In most cases, Smidt asks sellers to sign and send to him the claim forms for travel awards issued by each airline. In turn, he will mail back to the seller a contract specifying the details of their arrangement and a check for 50 percent of the promised price. He then submits the claim form to the airline in the name of the person who actually will be traveling. He will request a certificate for free business- or first-class travel, if this is what the buyer is seeking. In many cases, the airline will send the certificate to the seller, who then must forward it to Smidt. Smidt obtains a ticket for the buyer and mails the seller the balance of the payment.

Since such a process can be time-consuming, Smidt recommends that travelers who want to purchase broker-traded tickets apply several weeks in advance, if possible. Airlines limit the number of seats available for travelers using award tickets. The earlier you book, the better chance you have of getting the desired flight. Often awards can't be used during holidays and other blackout periods.

Travelers who cancel a trip cannot get a refund from the broker or the airline. However, says Smidt, the tickets generally are good for a year and departure dates can be changed.

"As in any industry, there are incompetent and unethical award brokers," says the association handbook, and Smidt agrees. He suggests steps travelers can take to protect themselves when dealing with brokers they don't know.

If you are selling mileage:

Shop around for the best price.

Make sure the broker sends you a contract and a deposit before you turn over the airline award certificates.

Ask if the broker is a member of the association. If not, find out why. Some very small brokers, such as Tickets to Go in Cambridge, deal only in a local market and have not felt the need to join.

Some airlines use sophisticated computers to try to detect trading in travel awards, says Smidt. Frequent flyers who claim numerous travel awards, but always request that the tickets be issued in someone else's name, are suspect. Conceivably, an airline may expel the frequent flyer from its award program.

If you are buying broker tickets:

Shop around for the best price.

Make sure the broker offers a refund on the ticket if an airline confiscates it.

If the broker accepts credit cards, charge your purchase. You can dispute the charge if the broker fails to provide the ticket for which you paid.

Get the name, address and phone number of the person whose travel award you are using. If an airline suspects you are using a broker ticket, says Smidt, you probably will be asked for this information as a way of testing you.

Don't reveal where you bought your ticket in the presence of airline personnel.

For a list of member brokers, contact the American Association of Discount Travel Brokers, 85 S. Union Blvd., Suite G300, Lakewood, Colo. 80228.