The crowd of students was warmed up first, as though that were necessary, by the school band and chorus. And when they exhausted a long list of patriotic songs and marches, the president of the United States walked on stage to talk of arms control, cultural exchanges and how well the United States and the Soviet Union would get along if the world were invaded by space aliens.

President Reagan came a-calling at Fallston High School here in Harford County this morning. And the students of this staunchly conservative town northeast of Baltimore, reacted with wild enthusiasm when he entered the school auditorium. They stood and clapped when he entered and left the room, they cheered, and they waved flags and signs saying "Yea to the U.S.A."

"I really admire him," said Alyson Moore, the 14-year-old freshman given the honor of introducing Reagan before the speech. "I agree with him 100 percent on what he says." Despite training in public speaking and drama, she said that before the president arrived, she was still painfully excited. She managed to fall asleep the night before, she said, only by repeatedly reciting the 23rd Psalm.

Reagan's speech summarized his talks with Soviet leader Mikhail Gorbachev two weeks ago in Geneva, but it concentrated on the possibilities for exchange programs between their two countries. "I want all of you, throughout America, to have a chance to meet and get to know your counterparts in the Soviet Union so that you can tell them all about this great country of ours," he said.

"I proposed to Mr. Gorbachev that we let young people from each country spend time in the other's schools, universities, summer camps and homes," Reagan said. "Americans would be able to see for themselves what life is like in the Soviet Union. And their young people would be able to see for themselves the freedom and openness of our society."

Apparently attempting to explain that the differences between the two countries, while vast, are surmountable, Reagan said he asked Gorbachev to consider what would happen if the earth were invaded by aliens from outer space.

"Just think how easy his task and mine might be in these meetings that we held, if suddenly there was a threat to this world from some other species from another planet outside in the universe," Reagan recalled telling the Soviet leader. "We'd forget all the little local differences that we have between our countries and we would find out once and for all that we really are all human beings here on earth together."

"Well, I don't suppose we can wait for some alien race to come down and threaten us," Reagan concluded. "But I think that between us we can bring about that realization."

After his 15-minute speech, Reagan answered the questions of a small group of students who had gathered to meet him in the school band room. Students there asked him his impression of Gorbachev, arms control and ways of reducing the risk of an accidental nuclear war.

During that discussion, Reagan signaled that the United States might stop adhering to the provisions of SALT II arms control treaty if the Soviet Union does not also adhere to the treaty. The issue has deeply divided his administration this year. "There's no way that we could be so one-sided . . . to stay within a limit that they are violating," he said.

Afterward, several students praised Reagan's speech, but said they were surprised that despite days of excited preparations and an inundation of advance staff, Secret Service agents and reporters, the president's visit was so short.

Student body President Susan C. Wood presented Reagan with Fallston's academic distinction badge -- a big capital letter "F" -- and the school mascot -- a stuffed toy cougar. Wood, who sat next to Reagan on the podium, said Reagan told her he was student body president at his high school.

Eric London, 15, a sophomore who sings bass in the Fallston school chorus, said it was thrilling to be visited by Reagan -- although it meant a lot of harried, last-minute chorus practices. He said he had been opposed to Reagan the first time he ran for office but has gradually warmed to him. "When the next four years are up, I'm worried about what's going to happen," he said.

Assistant Principal Thomas D. Proffitt said he wrote the White House about 18 months ago asking if Reagan would speak to his students. The 1,665-pupil school has a program in which prominent citizens speak to a class of students, and he thought Reagan would be hard to beat.

"Thanks but no thanks" was the reply, he said, but last month the White House called to see if the invitation was still open.

Proffitt said he not only stressed Fallston's high academic achievements when seeking the visit -- of the 1985 graduating class, 81 percent are continuing their studies and have received offers of about $190,000 in college awards -- but also the Fallston area's Republican credentials as well: Area residents voted more than 4-to-1 for Reagan, he said, and helped elect Republican Rep. Helen Bentley last year.