Margaret (Peggy) Goldwater, 76, the wife of Sen. Barry M. Goldwater (R-Ariz.), died Dec. 11 at Good Samaritan Medical Center in Phoenix of complications following surgery. Mrs. Goldwater had circulatory problems and had undergone two major operations recently, the amputation of her left leg and abdominal surgery.

In 51 years of marriage to Sen. Goldwater, the Republican presidential nominee in 1964, Mrs. Goldwater remained essentially a private person, although her husband was in public life for most of their marriage. She generally avoided press conferences and interviews, television appearances and campaign speeches, even when he ran for president. But she often traveled with him, and she came to practice the craft of the political handshake with a degree of deftness and aplomb even if she was not entirely comfortable with the process.

"I like politics," she insisted. "I love traveling around the country and meeting people."

Mrs. Goldwater was less than enthusiastic about leaving Phoenix after her husband was first elected to the Senate in 1952, but she moved her family to Washington in 1953 and took an apartment that soon became filled with his ham radio equipment and Spanish bullfighting posters.

In recent years she had spent most of her time in Arizona and California, finding the hot humid summers and the cold damp winters in Washington increasingly hard on her declining health.

Mrs. Goldwater, the former Margaret Johnson, was born in Muncie, Ind. She came to Washington when she was 16 to attend Mount Vernon Junior College and Seminary, now Mount Vernon College. She then went to New York where she studied painting for three years and worked as an apprentice fashion designer.

She met Barry Goldwater in 1932 while vacationing in Phoenix with her family, and married him two years later after a zany courtship that included a series of practical jokes and repeated marriage proposals. At one point when she was on a train en route to a medical convention with a group of doctors, the train was flagged down and a crate of apples was delivered to her seat. A note from Goldwater expressed the wish that an apple a day would keep the doctors away from the future Mrs. Goldwater.

On New Year's Eve 1933, she accepted his marriage proposal after Goldwater pushed his way into a telephone booth with her in Muncie when she tried to phone her mother to wish her a happy New Year. Goldwater declared he would never leave her side, nor would he let her out of the telephone booth, until she agreed to marry him. She said yes, and they were married the following September.

Years later Mrs. Goldwater would comment that "living with Barry Goldwater has been the most exciting thing that ever happened to me. He's full of surprises . . . . " Rearing four children in Phoenix, Mrs. Goldwater presided over a rambunctious family given to such stunts as firing toilet paper out of cannons and presenting each other with 200-pound pigs as birthday gifts.

She founded Planned Parenthood of Central and Northern Arizona. With her husband and family, she went deep-sea fishing and camping in the wilderness, and shot the rapids of the Colorado River in a rubber raft. She also liked doing needlepoint and playing bridge.

On Sept. 22, 1984, the 50th anniversary of their wedding, the senator was asked the formula for his successful marriage to Mrs. Goldwater. "You make the best of it," he said. "Realize they have their little peculiarities . . . . Say a little prayer every night."

In addition to her husband, Mrs. Goldwater is survived by two sons, former U.S. representative Barry M. Goldwater Jr. of California, and Michael Goldwater of Phoenix; two daughters, Joanne Butler of Phoenix, and Peggy Clay of Newport Beach, Calif., and 10 grandchildren.