When Alexandria Police Chief Charles T. Strobel goes on trial on obstruction of justice and perjury charges next month, federal prosecutors are certain to paint a different picture of the chief than did a special state grand jury that investigated Strobel last year.

That panel, advised by Fairfax County prosecutor Robert F. Horan Jr., not only absolved Strobel of allegations of wrongdoing, but also went on to praise him as an excellent administrator.

The contrasting actions of federal and state grand juries that investigated the 48-year-old chief, who has pleaded not guilty, and his police force have troubled and perplexed many residents of Alexandria.

There are several reasons for the different results. In the first place, the federal grand jury accused Strobel of lying during testimony that came several months after the state grand jury ended its six-week-long investigation.

In addition, the two grand juries had different roles and timetables. One examined allegations that the other decided not to pursue, and several key witnesses appeared before the federal grand jury but not before the state grand jury.

Some have said part of the explanation may rest in the two men who led the grand juries: Horan, who was special counsel to the state panel, and Acting U.S. Attorney Justin Williams, who directed the federal panel.

"One has been a cheerleader and the other is a methodical legal mechanic," said former Alexandria mayor Charles E. Beatley, long a Strobel critic, who believes Horan was not thorough enough in his investigation.

Beatley generally is thought to have lost his bid for reelection last May because of his repeated attacks on the chief and his calls for Strobel to be placed on leave. "The purple prose which came out of the special grand jury certainly came out with the stamp of Horan," since he directed the special grand jury, he said. Beatley was referring to its four-page report that exonerated Strobel and said his department was run in "a highly professional manner."

Robert Boraks, a Washington lawyer who represented two of Strobel's accusers, said the state grand jury's finding, that the chief's "principles of management" were strict but fair, was contradicted a few months later when a federal jury found that he violated the constitutional rights of two policemen by punitively transferring them. Strobel has appealed the case.

Horan stressed that the special grand jury "had a mind of its own," independently interrogating its witnesses. "I was not there when they debated and discussed their conclusions," and its final report "was handed to me in a parking lot in Lincolnia," Horan said.

"What Beatley has never understood in this whole thing," he said, "and it's probably why he got beat in the election, is that 11 citizens, totally independent of the political structure . . . and police structure of Alexandria listened to the witnesses and . . . drew their own conclusions. That grand jury report is the citizens speaking."

Alexandria City Council member Carlyle C. Ring said that the federal charges against Strobel are "pretty weak."

"I have serious doubts as to whether this is a sound indictment," Ring said, noting that the chief was accused of obstruction of justice "only because he said he could not remember particulars of a conversation 10, 12 years ago . . . . I can't remember what I did a few years ago."

The special state grand jury, which under Virginia law has no power to indict but can recommend indictments, was convened in January 1985 at the request of Alexandria Commonwealth's Attorney John Kloch amid political turmoil in the city following allegations, first published in the Alexandria Port Packet, that Strobel had halted an investigation into alleged cocaine dealing at a local restaurant frequented by Alexandria Sheriff Michael E. Norris.

The 11-member panel, working in the shadow of bitter political fighting at City Hall, heard about 30 witnesses in nine days of testimony over a period of almost six weeks. It found the allegations against Strobel, including the one that he stopped the cocaine investigation, "baseless and unfounded."

The federal grand jury began its investigation about the same time, after some of Strobel's accusers went to the U.S. attorney's office. It met once or twice a month over a period of slightly more than a year. Williams, who has consistently declined to comment on the grand jury's work, was later joined by a member of the Justice Department's Public Integrity Section.

The 67-page indictment that resulted from the investigation charged that Strobel testified "falsely and evasively" when asked about six occasions during the 1970s when he allegedly received reports of sexual misconduct by an Alexandria police officer and by two Fairfax County vice officers.

Several of the perjury charges stem from Strobel's testimony that he could not recall hearing the reports. He also was accused of lying to the grand jury when he denied stopping investigations into some of those reports, all charges he denies. Strobel, police chief since 1977, also is charged with obstruction of justice for each instance of alleged perjury. The federal grand jury investigated the 1984 cocaine probe, and did not charge Strobel with any wrongdoing.

Specifically, the reports that the indictment alleges Strobel received are:

That two Fairfax County police officers and an Alexandria officer were sexually involved with a prostitute.

That the same Alexandria policeman had attempted to rape two women on two occasions.

In the first alleged assault, the indictment contends that Strobel, then head of the Alexandria Police Department's internal affairs section, "willfully . . . covered up" the alleged attempted rape; and that in the second alleged assault, he allegedly made a false statement in an internal report complaining that the woman had waited more than a year to come forward, knowing that to be untrue.

Horan said a witness before the state grand jurors told them he had given the federal grand jury a tape recording that contained the allegation about the policemen's alleged involvement with a prostitute.

As a result, he said, the state grand jury decided not to investigate these allegations, or Strobel's handling of them, because the federal panel was looking into them. "It was our position that we weren't going to investigate what the federal grand jury was investigating," he said.

Horan said that the special grand jury "had some testimony" about the two alleged attempted rapes by the Alexandria officer. Asked whether Strobel was questioned about how he handled the reports, Horan said, "I believe he was."

Because of its different handling of these reports, the state panel did not hear from several persons whose testimony apparently contradicts Strobel's, and apparently forms the basis for the federal perjury charges as described in the indictment.

Among those witnesses are former Alexandria police sergeant Alfred Davis, Alexandria police Sgt. Larry Brohard and Rockville Deputy Police Chief Capt. John Miller, formerly of the Alexandria force. All three said they did not appear before the state grand jury.

In addition, the woman who originally made the allegations about the three officers' relationships with the prostitute appeared before the federal grand jury but not the state panel, sources said.

Despite the two grand jury probes, some matters remain unexplained. For example, a full explanation of how the cocaine investigation came about and was conducted has not been publicly given. "That's a mystery which should be unraveled," said Beatley.