In fall 1983, an Alexandria police investigator says, he heard allegations that cocaine was openly used at Marco's Cafe, a popular restaurant on South Washington Street, and that Sheriff Michael E. Norris was seen frequently at the restaurant.

A police investigation into those allegations was begun, and then, in April 1984, it was abruptly halted without explanation, according to Charles Cox, one of two investigators assigned to the case.

That short-lived investigation set the stage for what has become a royal political battle. The controversy over the allegations has preoccupied top levels of the Alexandria government and put several jobs in jeopardy.

On Tuesday, a special grand jury will convene to review the drug investigation, attempting to answer questions that have set city officials against each other and have been the talk of the town for weeks.

The grand jury's main task will be to determine whether there was misconduct on the part of any city official in connection with the drug investigation, particularly whether misconduct was involved on the part of Public Safety Director Charles T. Strobel or his boss, City Manager Douglas Harman. Both have denied any misconduct. In the process, the grand jury will attempt to find out how and why the investigation was started, what its purpose was and why it ended when it did.

What they find out, city officials hope, will determine the truth about a police investigation that has been described by some as a good-faith effort, albeit poorly planned and executed, and by others as a politically motivated investigation in an attempt to discredit Norris.

The following recent events led to the convening of the grand jury:

At a closed City Council meeting on Dec. 11, Donald C. Casey, a Democrat, says, he told fellow council members about allegations that the drug investigation had been improperly handled. Casey had been briefed on the allegations, he said, by Alicia Mundy, a reporter for the community newspaper that first published the allegations, the Alexandria Port Packet.

At the meeting, Casey says, he told council members that there were allegations that Strobel had quashed a police drug investigation when the names of Norris, a Republican, and another high-ranking police officer turned up on tapes made by a confidential informant in the drug case.

Casey says he called in Strobel, Harman and Commonwealth's Attorney John E. Kloch separately to answer questions about the drug investigation. Casey says he was dissatisfied with their answers.

Harman says that Casey had not told the officials exactly what he was seeking in his questions during the closed council meeting. "It was not clear what the issue was," Harman said recently.

On Dec. 20, the Packet disclosed allegations made by former police investigator Cox that the drug probe had been stopped prematurely.

The following day, Strobel and Kloch held a joint news conference at which Strobel said that: A police investigation into drug trafficking at a city restaurant began in late January 1984 and was still going on. Norris was not the target of the investigation, but his name had surfaced during the investigation.

Both Kloch and Strobel stressed that none of the evidence produced by the drug investigation indicated any criminal wrongdoing on Norris' part.

Cox agrees that there was no evidence of criminal activity by Norris when the investigation was terminated. But he says there were enough leads both about Norris and about drug activity on the part of others that the probe should have been continued.

Former employes of Marco's have said in recent interviews that it was fairly well known that drugs were being used at the restaurant, but that it purportedly occurred mainly in the kitchen and back offices.

At any rate, they say that the illegal activity stopped in January 1984 when a new owner began managing Marco's.

The day after Strobel's news conference, the City Council met in emergency session and unanimously voted to hire a lawyer to independently review the handling of the drug investigation. In addition to Strobel and Norris, the review was to include Harman because he is Strobel's superior.

Some City Council members have expressed concern that Harman did not brief them on the continuing drug investigation at a time when he was asking them to merge the sheriff's office into Strobel's Department of Public Safety.

Cox has alleged that in early April, a few weeks before the council voted to merge the two departments, he and the other investigator, Philip Adcock, "kept getting pressure that if we were going to make a case against Norris , they wanted it done because the merger was coming up."

But when the City Council met Jan. 3 to implement their decision to hire a lawyer, the three Republican members had changed their minds. Along with Harman, they argued that the allegations were of a criminal nature and therefore ought to be reviewed by city prosecutor Kloch.

Although the four Democrats were ready to vote for an outside investigation, Mayor Charles E. Beatley declined to call a vote, saying he did not want to proceed without a consensus on such an important issue.

Harman then said he would formally ask Kloch to review all the allegations surrounding the drug investigation. Kloch agreed and began work the next day.

However, Kloch came under fire from Cox, who has since left the force, and two other policemen who are familiar with the case. They said they had briefed Kloch on the allegations in October and that he had failed to find any wrongdoing on Strobel's part.

Kloch said he sent a tape recording of his October conversation with the policemen to the Virginia State Police for review.

Kloch, faced with the tricky situation of investigating the actions of his chief law enforcement officer, decided Jan. 7 to ask for a special grand jury to review all allegations surrounding the drug investigation.

The special grand jury is likely to ask Circuit Judge Donald H. Kent, who impaneled the investigative body, to appoint a special prosecutor to conduct their investigation.

The City Council last week asked Kloch to urge Kent to make public as much as possible of the grand jury's final report.

As an independent and autonomous body, the grand jury "can go virtually anywhere it wants to go" in its investigation, Kloch told the City Council last week.

Meanwhile, the new owner of Marco's Cafe, Abby Sadeg, last week celebrated his first year in the restaurant.

"The only mistake we made," he said recently, "was we kept the name."