Alexandria businessman Robert S. Richard was awakened at two in the morning recently by a man he describes as "drunk out of his mind" who had staggered into the vestibule of the small apartment building in Old Town where Richard lived.

"He was yelling obscenities and banging on the glass doors," Richard said. "He passed out several times, then woke up twitching. When I told him to leave he threatened to kill me. He left before the police arrived," Richard said.

That incident and others in which Richard said he witnessed people yelling on the streets, urinating on parked cars, and leaving their vans in private driveways with "the stereo turned up at top volume," were among the reasons Richard and his wife recently move to Annapolis.

Similar incidents, which some Old Town residents complain are occuring at an alarming frequency, are the subject of what is expected to be a heated debate in Alexandria in the next few months.

"I have had some complaints in the past few months," said Mayor Charles E. Beatley Jr. "A fair number of people come over here from Washington and Maryland thinking this is an area for fun. Many of them don't even go into the restaurants, but just drive around the streets, or hang out near the bars. Along with the attractions of Old Town you have some problems.There's no such thing as purity," he said.

The irony in the situation, Beatley and others point out, is that for years the Old Town area suffered from lack of commercial business. Now it is favorably compared to Georgetown for its wide variety of restaurants, shops and stores.

One defender of the business in the area, Robert Bellevance, executive director of the Alexandria Chamber of Commerce, says flatly, "There is no problem . . . Most other communities in the United States would do anything to have the business district we have in Old Town."

The lower King Street area, adjacent to the Potamac River, has become an increasingly popular night life area, according to merchants, police, and some embittered residents of nearby town houses that frequently sell for more than $200,000 apiece.

Last year 14 restaurants in the 16-block area bounded by Prince, Princess and Pitt streets and The Strand in Old Town had gross receipts of $11.7 million, according to city Finance Director Howard Holton. The figures for 1979 are expected to be considerably higher, he said.

Last month Alexendria police made a record 38 arrests for public drunkenness, six arrests for other misdemeanor violations and issued 489 parking citations, according to Deputy Police Chief Arlen Justice.

As a result of citizen complaints about public conduct in the area, where the claims of safe streets and a quiet style of living are used in sales pitches by real estate agents, police recently assigned two patrolmen for the first time to walk a beat in the area. The foot patrol concentrates on the area around restaurants, Justice said.

"The problems have increased gradually over the past two or three years, but now they are terrible," said Prince Street resident Lonore Van Swearingen. She has prepared a list of alleged incidents in the area, which she said include two incidents of sexual activity on city streets, broken windows, beer cans and other debris scattered on front door steps and attempted break-ins.

Tonight the City Council will consider whether to appoint a panel of citizens and business people to investigate the situation.

According to Van searingen and other critics, many of the problems stem from the fact that under state law restaurants are forbidden to earn more than half of their gross receipts from the sale of alcohol. Beer and wine are not included in that equation, meaning that unlimited amounts of beer and wine can be sold by restaurants.

Tonight the council will also consider asking the state Alcohol Beverage Control Board to change its rules and include beer and wine under its category of alcoholic beverages.