Gertrude Eggimann, a 66-year-old Swiss widow visiting Washington with a tour group, had finished dinner and was taking a stroll near her Southwest Washington hotel last year, when she and two elderly companions were accosted from behind by a man with a gun.

When the man demanded their pocketbooks, a struggle ensued and Eggimann was shot in the stomach. She died an hour later at George Washington University Hospital.

Yesterday in D.C. Superior Court, Chief Judge H. Carl Moultrie I sentenced Harold L. Beynum, 28, of the 900 block of Third Street SW, to serve 41 years to life in connection with the May 1981 slaying of Eggimann, another assault three hours earlier in the parking lot of the same hotel, and three other crimes.

Beynum was found guilty of the killing last Oct. 7 by a Superior Court jury, which also convicted him of assault with intent to kill another guest of the hotel, the Skyline Inn, at 10 I St. SW. The guest, James Stamateris, a Navy employe from Pennsylvania, testified that a would-be robber had pointed a gun at his stomach and pulled the trigger, but the gun misfired.

Assistant U.S. Attorney William J. Bowman, who described the killing in court as a "deliberate and cold-blooded murder for which the defendant has never shown any remorse," said Beynum will not be eligible for parole for 41 years as a result of consecutive sentences imposed by Moultrie.

In asking the judge to impose consecutive sentences, Bowman noted that Beynum was also indicted last week in connection with another slaying that occurred less than a week after the Eggimann killing. In that one, Beynum was charged with killing Reginald Hayes of Temple Hills, who was shot twice in the chest and whose decomposed body was found in June 1981 in a wooded area in Southeast Washington.

Before sentencing, Beynum's lawyer, Jennifer Lyman, had asked the judge to consider the fact that Beynum had no previous convictions for crimes of violence. She said her client maintains his innocence and plans an appeal.

Beynum was sentenced to serve 20 years to life for murder, seven to 25 years for assault with intent to kill, two terms of five to 15 years for assault with intent to commit armed robbery, three to 10 years for carrying a pistol without a license, and one to five years for assaulting a police officer. The last charge was in connection with Beynum's capture by police June 10, 1981.