A "hopelessly deadlocked" all-white federal jury could not reach a verdict Monday in the trial of three U.S. border patrolmen accused of systematically beating Mexican immigrants and depriving them of their civil rights.

The deadlock, 11 to 1 for convicting two of the patrolmen and 10 to 2 for convicting the other, came despite testimony from three Border Patrol trainees that they witnessed the planning and carrying out of the beatings in question.

The indictments were the first ever filed in federal court for civil rights violations in the Border Patrol's 55-year history, and the trial was attended by droves of off-duty patrol agents who sometimes expressed their sympathy for the defendants by laughing or expressing sounds of disbelief at the testimony of prosecution witnesses.

U.S. attorney Michael H. Walsh, the prosecutor, said today that "a resonable offer" would be made to the defendants allowing them to plead guilty to one of the charges against them. If they do not plead, he said, the case will be retired.

"The result of this trial shows that it's damn tough to convict a border patrolman of abusing aliens," said Walsh. "But we're going to keep at it. I'm happy that 11 of the 12 jurors were presuaded by the evidence -- and there might not be a holdout the next time."

The lone holdout on the most serious charge was a woman said by other jurors to be unwilling to discuss the evidence. All prospective jurors who were either young or members of minority groups had been exluded by defense challenges. The youngest juror was 47 years old and white.

The prosecution attempted to show that a small core of Border Patrol agents have planned and executed "vigilante justice." A transcript of a radio conversation showed defendant Jeffery Otherson saying to defendant Bruce Brown that he was "Delta Henry" -- the code words for the "designated hitter" who had the responbility of inflicting punishment on apprehended aliens.

Border Patrol trainees testified that they saw an immigrant who supposedly had made an obscene gesture at a Border Patrol plane beaten on the hand with Brown's nightstick until it was swollen to the point that the knuckles couldn't be distinguished from the rest of the hand.

However, the prosecution was unable to find the beaten immigrant. He along with other reported victims, was returned to Mexico after the incident.

Attacking the indictment, defense attorney Nelson Brav said it was "government hypocrisy" to try the patrolmen, who must guard a 12-mile stretch of border that an estimated third of a million aliens cross each year with nothing more serious than a wire fence to discourage them..

In the prosecution view, the trial was conducted in an unfavorable political climate created when American hostages were seized in Iran. Locally well-publicized events during the trial included the cutting back of Border Patrol expansion by the U.S. Office of Management and Budget, and the stoning from the Tijuana side of the border of a Border Patrol detail evacuating a wrecked helicopter and its crew.

Even without the influence of such external events, it always has been difficult to win convictions in cases involving Border Patrol actions against Mexicans. Last April a local jury acquitted a patrolman of a charge that he shot a Mexican in the back. The verdict confirmed militant Chicanos in their belief that illegal immigrants do not enjoy the effective protection of U.S. law.