Arlington businessman Thomas J. Broyhill built the American Realty Trust into a major hotel/motel owner in the Washington area, only to watch the firm crumble in the last two years under law suits from creditors and the Securities and Exchange Commission. Yesterday, he told stockholders who have stuck by him that they won't be sorry.

Looking robust and sounding reinvigorated after a recent scare over cancer, Broyhill, 67, predicted that within 90 days his company will have settled its troubles with short-term creditors and be trading again on the American Stock Exchange.

The occasion for Brohill's optimism was the first shareholder meeting since the real estate trust - one of the first of its kind when it was formed in 1961 - became embroiled in a series of law suits charging a list of actions more tangled than a bowl of spaghetti.

Those troubles began in July 1975 when three of the trust's eight directors resigned in a huff, complaining that Broyhill was operating American Realty as if it were his own firm and without telling them the whole truth about company business.

Six months later, the SEC filed a complaint charging American Realty and Broyhill with defrauding shareholders and concealing from them information necessary to protect their investments. The SEC asked that Broyhill be removed as president and chairman of the trust.

But the SEC lost in court and, though the case is on appeal, Broyhill yesterday declared the battle over.

"I expect no more problems from any source," he told several dozen shareholders seated in a conference room in Crystal City's Hospitality House, one of six hotel/motels American Realty owns in the Washington area. The trust also owns office buildings in St. Louis and Charlotte, vineyards in California, marinas in Virginia Beach, a tract of land in Atlanta, and 10 Gino's Restaurants (most of which are in California) plus several other holdings.

The trust is anxious to sell some of these properties, but the problem is to find a bidder who will offer a respectable price, Broyhill said.

The trust has decided to operate other properties, such as its Williamsburg Hospitality House, directly for income purposes. To do this, it has had to forego its real estate investment trust status and has been taxed as a normal corporation instead.

Despite some progress in operating results and sharply curtailed losses, American Realty is still short on cash. Broyhill conceded the trust has fallen behind in interest payments on several bank loans and bond commitments, and owes more than $200,000 on a sinking fund payment that was due last December.

All but one of the trust's banks, have been patient, Broyhill said. The company is on the verge of closing a comprehensive refinancing agreement under which it would pay off one-third of its current short-term debt and remainder would be extended.