Barry and Shirley Sheehe bought a "time-share interval" in an Ocean City apartment building last May, agreeing to pay Seatime Associates Inc. $5,920 for use of an apartment for one week each year. Last week, the Annapolis couple learned that the real estate marketing firm had sold the same apartment for the same period to a Baltimore woman in July 1979, according to Maryland authorities.

And Richard J. Fallica of Riverdale bought one week's worth of time from the real estate marketing firm in May 1981, paying what he called a "pretty attractive" price -- $2,100 -- for use of a one-bedroom apartment for one week each year. An added attraction for Fallica was the opportunity to trade his time at Ocean City for visits to other vacation spots. Last week, he learned that the state officials believe Seatime Associates never owned the apartment it sold him.

The Sheehes and Fallica are among an estimated 1,000 to 1,500 buyers who are in danger of losing their investments, ranging from $2,000 to $8,000. They are the victims of fradulent sales practices by Seatime, say Maryland authorities. Auditors from the state real estate commission are sifting through Seatime records, compiling a list of purchasers who are affected.

The commission and the state Consumer Protection Division filed suit last week in Worcester County Circuit Court, charging that Seatime sold intervals in units to which it does not hold a clear title, sold time shares in three units that it never owned and, in some instances, sold space in the same apartment for the same period to more than one person.

In the type of time sharing sold by Seatime, a customer buys a fractional interest -- usually for one or two weeks -- in a resort condominium on a long-term basis. The buyer receives a deed for his share of the property. Another kind of time sharing is the purchase of "right to use" interest in vacation properties, including condominiums, hotels, motels and yachts. Owners can trade their vacation periods and facilities, often using the resources of "space banks" established by firms set up to help time sharers swap vacations.

Before its difficulties last week, Seatime handled sales in 54 of the 100 condominiums in two buildings known as Seatime North and Seatime South, taking advantage of the soaring interest in the purchase of fractional ownership of vacation property that made time sharing a $1.3 billion industry last year.

According to court documents, Seatime has bought 29 of the condominiums since 1976. The company negotiated for the purchase of "approximately" 25 apartments that title to the units was encumbered by debt, and also failed to use money paid by the customers to pay off the mortgages, according to the documents. Foreclosure on the units is threatened by Seatime's debt, which a state official placed at "around $800,000.

"We haven't pinned down where the money went," said H. Robert Erwin Jr., chief of the state consumer agency.

Seatime Associates is insolvent, and the whereabouts of its former president, Kenneth Puckett, are unknown, according to the documents. Retired circuit court judge Daniel T. Prettyman was appointed receiver to direct the company's affairs.

Through the receivership, "We hope to avoid total financial collapse and bankruptcy," said Erwin.

State authorities hope "that, by working with creditors . . . and by infusion of additional cash from new investors or sale of additional time shares where title can be conveyed . . . enough money can be generated to pay off the old mortgages," Erwin added.

Despite a sagging real estate market, time share sales are moving along at a respectable rate and are expected to reach $1.5 billion this year, according to the National Timesharing Council.

Francis X. Pugh, an assistant attorney general assigned to the case, said the Real Estate Guarantee Fund, established to aid people who have been damaged by the misconduct of licensed brokers and salesmen, is another possible source of relief for buyers. The Real Estate Commission must decide whether Seatime customers would be eligible for compensation from the fund, Pugh said. He added that the fund contains about $1.25 million, with some pending claims, and could be depleted severely if it were used to cover Seatime's estimated $800,000 in debts.

Pugh estimated that "three to four weeks" may be needed to pin down the names of all the affected buyers who live "all over the country and in foreign countries."

Some of those buyers say they had indications that all was not well with Seatime before the state's court action last week. Silver Spring resident Jack Leonard said he repeatedly asked for a paid-and-cancelled note and a deed to his property last spring after he had paid in full for his one-week share of a Seatime unit.

Finally, Leonard said, he threatened to complain to the real estate commission. Within a few days, Seatime sent him a letter stating that his unit was paid for, but he has never received a canceled note, he said, adding, "And I still don't have a deed."

Fallica said he told the company he wanted to trade his share in a one-bedroom condo for a share in a three-bedroom unit when one became available. He said he was sent bills for maintenance of a three-bedroom apartment but never has received a deed.

The action against Seatime alleges that the company violated provisions of the state's consumer protection act. Maryland is among the majority of states that have not passed laws regulating the time share industry. Erwin said state officials will decide between now and January, when the state legislature convenes, whether they will press for legislation designed specifically to govern time share sales.

Time sharing is a relatively new vacation industry in this country. The idea originated in Europe, and most U.S. organizations have been formed in the last six years. A few states with popular vacation areas, such as Flordia, Hawaii and California, have regulated time sharing, usually by requiring that developers file advertising copy with a state agency, that sales proceeds be placed in an escrow account, and that sales persons be licensed, among other rules.

Only one other time-sharing organization has been taken to court in Maryland. The Montgomery County Office of Consumer Affairs filed suit against Southair International Club, Inc., and former Washington Redskins professional football player Michael T. Bass, the head of the club, in 1979, alleging that the club failed to provide vacation accommodations as promised or sent vacationers to condominiums that were unsafe and unsanitary. The case has not yet come to trial.

Virginia legislators passed a time-share act in 1981. With only four time-share projects in the state -- one seaside resort, two mountain vacation spots and a campsite -- Virginia has had few problems with the industry, said a spokesman for the state Real Estate Commission.

"The main thrust of our complaints are the typical Monday morning buyer's remorse," in which a purchaser decides he or she can't afford the time-share resort after all, said the spokesman. He added that developers in the "not too distant past" usually were willing to work out a way to release such buyers from at least a portion of their obligations. "Now times are a little rougher in the real estate business," and developers are holding buyers to their contracts more often, the spokesman said.

No cases of fraudulent practices in time-sharing sales have been reported in the District of Columbia, said an officer of the consumer fraud unit of the police department. Last June, Barclay Properties Inc., the first company to sell time-share units in Washington, filed for bankruptcy and returned purchase money to people who had bought shares. Company officers said their lender, FSI Financial Group, was unable to release agreed-upon funds for the final sale, and that a sluggish market had hampered sales.

The National Timesharing Council favors industry regulation by the states, and has drafted model legislation.