After graduating in 1945 from St. Thomas High, an all-male Roman Catholic prep school in Houston, Mr. Archer attended Rice University, then transferred to the University of Texas at Austin, where he earned a bachelor’s degree in business administration in 1949 and a law degree in 1951.
Mr. Archer was in the Air Force during the Korean War from 1951 to 1953, rising to the rank of captain.
In 1953, he married Patricia Moore. They had five children, Richard, William Reynolds III, Sharon, Elizabeth and Barbara, and were divorced in 1981. In 1983, he married Sharon Sawyer, who had two sons by a previous marriage, Scott and Shannon. Information about his survivors was not immediately available.
Mr. Archer was the president of Uncle Johnny Mills, the family feed business in Houston, from 1953 to 1961. From 1955 to 1962, he was a councilman and the mayor pro tempore of Hunters Creek Village, an affluent suburb of Houston. In 1967, he was elected to the first of two two-year terms in the Texas House of Representatives. He switched from the Democratic to the Republican Party in 1969.
In 1970, he was elected to Congress from the Seventh District in Texas, succeeding George H.W. Bush, the future president, in the traditionally Republican seat, with 65 percent of the vote. He was re-elected 14 times, and his vote share never dropped below 79 percent. He did not seek re-election in 2000.
After leaving Congress in early 2001, Mr. Archer became a lobbyist in Washington and a senior policy analyst for PricewaterhouseCoopers.