Psychiatrists today said David Berkowitz is mentally incompetent and incapable of standing trial for the murders of six young men and women attributed to the night-stalking gunman Son of Sam."

State Supreme Court Justice Gerald Held read the conclusions of psychiatrists who have studied Berkowitz since his arrest and set Oct. 4 for the start of formal hearings to determine if the pudgy 24-year-old postal worker must stand trial for the shooting death of the last of Son of Sam's murder victims.

The eight-page report, signed by two court-appointed psychiatrists who examined Berkowitz for 11 hours, concluded that he suffers from paranoia, and said his prognosis is "guarded."

"Said defendant, as a result of mental disease or defect, lacks the capacity to understand the proceeding against him or to assist in his own defense," the doctors said in their report.

Those are the criteria for competence to stand trial in New York state.

If the findings stand, Berkowitz would be ordered incarcerated in a state institution for the criminally insane. He would not be brought to trial unless he later were judged to have recevered his sanity, which the psychiatrists said was questionable.

However, Brooklyn District Attorney Eugene Gold won the right to have his own psychiatrists examine Berkowitz.

"As the district attorney of this court," Gold said, "it is my opinion that Mr. Berkowitz is fit to stand trial."

Judge Held gave the state until Oct. 4 to present any conflicting psychiatric data that might open the way to a trial. In New York, the Supreme Court is a trial court and the Court of Appeals is the highest state court.

The murders of six young people, and the wounding of seven others, were carried out over a year of terror, always at night and with a .44-cal. revolver. The gunman concentrated on couples in parked cars, and sometimes left taunting notes for the police and the media, eventually adopting the name "Son of Sam."

Berkowitz, who was arrested Aug. 10 after a parking ticket issued near the site of one killing led police to him, came to court this morning with an escort of nine police cars and a police helicopter.

He displayed no reaction during the brief legal proceedings as his alleged mental shortcomings were read from the letter covering the psychiatrists' eight-page opinion.

Held read from the cover letter of the report in court, but ordered that the document be resealed and that those familiar with it not discuss it.

Berkowitz is under indictment in Brooklyn for the last of the .44-cal. attacks - a July 31 assault that killed Stacy Moskowitz, 20, and partially blinded her date, Robert Violants, 20.

In addition, Berkowitz has been indicted in the Bronx for three murders and the wounding of a fourth person and in Queens for two killings and five woundings.

The Bronx and Queens indictment are being put off pending a finding in the Brooklyn case. Court sources said a finding that Berkowitz is incompetent would shelve those indictments.

After today's court sesson, Berkowitz was returned to an isolation ward at Kings County Hospital, where he has been confined since his arrest.

The psychiatrist, Dr. Daniel W. Schwartz and Dr. Richard L. Weiderbacher Jr., said they examined Berkowitz for a total of 11 hours at the hospital.

They also spoke with the defendant's father, Nathan Berkowitz, who adopted Berkowitz when he was 17 months old.

The doctors studied statements Berkowitz has made to prosecutors, photographs of his Yonkers apartment and automobile, skull X rays and brain tests, and Son of Sam's letters to police and Daily News columnist Jimmy Breslin.