Allegations of crime syndicate influence in City Hall here have led to the resignations of two of Mayor Jane Byrne's top aides and have plunged her troubled administration into its potentially most serious crisis.

The aides, William Griffin, chief of staff, and Michael Brady, legislative liaison officer, abruptly quit Monday night saying they no longer possessed "the trust or confidence in the mayor needed to perform our duties."

Griffin and Brady said they would cooperate with a grand jury investigation into charges that top police officals had been transferred or demoted under pressure from a Democratic committeeman who is a longtime associate of crime syndicate figures.

The charges came over the weekend from former acting Police Superintendent Joseph DiLeonardi, once a Byrne favorite but now out of favor with the mayor. He charged he had been ordered by Griffin to transfer the deparment's organized crime expert from his deputy superintendent's post because he was upsetting First Ward Committeeman John D'Arco.

Byrne, who accepted the resignations of her two aides today "with regret," was said to have been distressed at their decision to leave.

Brady, a former Illinois legislator, and Griffin, a former reporter for The Chicago Tribune, had been increasingly frozen out of power in recent months after Byrne's newspaperman husband, Jay McMullen, was hired to become her political consultant and press secretary.

Their loss of power was believed to be a part of the resignation decision as well.

State's Attorney Bernard Carey, who is running for reelection in November against Byre antagonist Ricahrd M. Daley, son of the late mayor Daley, said the grand jury would attempt to establish whether there had been any obstruction of justice.

Bryne had said she would testify before any grand jury, saying she is "clean as a whistle." She described the allegations of the policemen as an internal squabble, saying, "I'm not going down as a friend of the mob."

But the confusing array of charges left Byrne and her now deposed aides pointing finers at one another.

Byrne suggested to reportes Sunday, amid DiLeonardi's charges of forced transfers, that perhaps her aides, Brady and Griffin, had conducted city business without her knowledge.

In resigning Monday night, Griffin and Brady quoted DiLeonardi as saying Byrne had ordered him to make other politically motivated moves in the department. They quoted the former police chief as saying, "believe me, the things I could tell you that I was asked to do by the mayor, you wouldn't believe it. I could blow the lid off."

The decision of DiLeonardi, who was joined by two other top officers to publicly air charges of mob meddling, followed by only a few days the demotion of the officers by Byrne's newest police superintendent, the fourth in one year, Richard Brzeczek.

Brzeczek said his "management style" differed from that of DiLeonardi and the others.