NEW YORK (AP) _ A state judge on Wednesday granted an annulment to former Metropolitan Opera impresario Sir Rudolf Bing over the objections of his mentally ill wife, ending their 33-month marriage.

The 87-year-old Bing, who suffers from Alzheimer's disease, and Carroll Douglass, 50, had lost touch with reality, their attorneys told Judge Carmen Ciparick.

Bing is in a nursing home and Ms. Douglass is hospitalized in a psychiatric ward.

Ciparick also denied Ms. Douglass any part of the Bing estate or alimony, said her attorney, Harvey Sladkus.

The judge ordered Bing's estate to pay the expenses for Ms. Douglass' hospitalization for mental problems last summer, Sladkus said.

''I haven't spoken with her yet, but we can still go before the appellate court or make a motion to re-appeal,'' said Sladkus. Ms. Douglass' sister and brother in Washington will also confer on the next legal move, Sladkus said.

Bing's attorney, Paul Goldhamer, said he was gratified by the judge's decision, but was sorry it took so long. The annulment trial began in May 1988 and closing arguments were made March 15.

''Time is certainly not on Sir Rudolf's side,'' Goldhamer said. ''It's a great tragedy that could only have happened under these peculiar circumstances.''

Bing's legal guardian, Paul C. Guth, was on vacation and was not available for comment.

Attorneys for Bing, the opera's general manager for 22 years, had claimed he was mentally incompetent and had no idea what he was doing when he married Ms. Douglass on Jan. 9, 1987, in a civil ceremony in Arlington, Va.

Almost half the couple's marriage was spent in court.

During the annulment trial, a psychiatrist testified that Bing was suffering from Alzheimer's disease and did not recall being married.

Ms. Douglass was hospitalized last August after she ''lost touch with reality,'' her lawyer said.

Goldhamer charged that Ms. Douglass had abused her husband verbally and physically during the early part of their marriage.

Ms. Douglass' erratic behavior during the trial compelled Ciparick to bar her from seeing Bing for six hours each day.

Earlier this year, Bing was forced to sell off a Grandma Moses painting worth more than $35,000 to cover the cost of the nursing home.

Goldhamer said his client's funds were depleted because Bing had to hire guards to keep Ms. Douglass away.