Avon C. Alexander, 59 was convicted in D.C. Superior Court yesterday of second-degree murder in the slaying of a 26-year-old undercover police officer who was shot once in the back of the head during a narcotics investigation.

The jury of six men and six women deliberated for 12 hours before it found Alexander, who lived at 4347 Martin Luther King Ave. SW, guilty of murdering Officer Bruce W. Wilson, a five-year veteran of the metropolitan police force, last April.

Alexander, who did not know Wilson was a police officer at the time of the shooting, also was convicted of two counts of carrying a pistol without a license.

The week-long trial provided a glimpse of the risks of undercover police work in the underworld of narcotics.

Alexander claimed that he shot Wilson in self-defense. According to testimony, he told police that he thought Wilson was a "stick up bou" involved in the robbery and kidnapping of a friend of Alexander - who allegedly had just sold narcotics to Wilson.

At the end of the trial, Judge Eugene N. Hamilton refused to allow the jury consider the issue of self-denfense, because, Hamilton said, the evidence was insusfficient to support that contention.

Judge Hamilton also refused to allow the jury to consider the lesser charge of manslaughter, despite arguments by defense attorney R. Kenneth Mundy who said the shooting could have been an accident. Mundy also argued that Alexander could have fired not out of malice but because he was upset over the assault on his friend.

According to the government's case, Wilson, who was investigating drug distribution in the far Southwest area, made a drug buy on the afternoon of April 25 from a friend of Alenxander, known as Jim Flint.

Assistant U.S. Attorney Ted Shmanda told the jury that Wilson wanted to protect his identity, so he sent other plainclothes policemen to arrest Flint.

The two police officers confronted Flint in the basement of an apartment building at 205 Elmira St. SW and a scuffle ensued.

Alexander and two other men were in a nearby office. One of the men heard the commission, looked out into the corridor, then went back to the office and said "the stick-up boys" had jumped Jim Flint.

The two plainclothes officers took Flint out of the building. the government contended that Alexander went to an apartment in the building and got a gun.

Alexander then went to a basement entrance of the building where he came upon Wilson talking to a maintenance man, Freddie Lee (Dog) Perry. Perry told Wilson he better leave because "the stick-up boys just came."

Wilson hesitated and then turned and walked away. Alexander then called out 'Hold it man! Hold it!" The government argeud that Alexander fired when Wilson refused to stop.

According to testimony, Alexander tod police that just before he fired at Wilson, the police officer reached for his coat.

Mundy tried to establish that Wilson had started to turn towards Alexander. The combination of the two actions, Mundy contended, could have led Alexander to shoot in self-defense because he thought that Wilson was reaching for a gun and turning to fire.

Perry testified that Wilson did not turn and did not appear to reach for anything.

The defense put on no evidense during the trial. Alexander did not take the witness stand in his own defense. If he had, Mundy said, the prosecutor could have questioned Alexander about his lengthy criminal record, which dates back to 1938.

Shmanda argued that Alexander was guilty of first-degree murder because he said the killing was planned and deliberate. he contended that Alenxander got the gun and then, like a "self-professed vigilante," shot Wilson when he refused his order to stop.

In finding Alexander guilty of second-degree murder, the jury determined that Alexander killed Wilson with malice but not with premeditation.

Judge Hamilton said he will sentence Alexander on Sept. 14.

The murder charge carries a maximum penalty of life imprisonment. Because he had previous felony convictions, Alexander could be sentenced to life prison terms on the gun convictions.