Two groups of demonstrators, totaling about 475 persons, marched, carried placards and chanted slogans in a day-long protest here yesterday against the shah of Iran. No unusual incidents were reported.

Authorities said about 250 persons took part in a demonstration sponsored by the Iranian Student Association in protest of what the marchers described as murders of Iranians carried out recently by the shah's government.

In addition, authorities said, another 225 persons participated in a demonstration sponsored by the Young Muslims Organization, aimed at protesting what participants called "gross violations of human rights in Iran."

During yesterday's demonstration, the student group marched to the area of the White House, then past the State Department to the Pentagon where they protested against U.S. sales of arms to iran and shouted such slogans as "U.S. Get Out of Iran." Many of the protesters were masked.

In the late afternoon, demonstrators marched to the vicinity of the Iranian Embassy on Massachusetts Avenue NW before disbanding. There were reports of snarled traffic near Massachusetts Avenue and 34th Street, authorities, said.

During the marches, demonstrators were flanked, followed or confronted by District police, U.S. Park Police, General Services Administration police and the uniformed division of the Secret Service (formerly the Executive Protective Service).