Frank Reynolds, 59, an anchorman of ABC television's "World News Tonight" since 1978 and a broadcast journalist for more than 30 years, died of viral hepatitis and bone cancer yesterday at Sibley Memorial Hospital.

Mr. Reynolds joined ABC in 1965. He last appeared on "World News Tonight" on April 21. His coanchors on the program were Max Robinson in Chicago and Peter Jennings in London.

He was regarded by colleagues as a knowledgeable and consummate professional.

On camera, his appearance and manner were formal and he conveyed a combination of quiet authority and concern, whether the news was high tragedy or the sometimes comical commonplaces of everyday life. His nickname was the "Gray Ghost."

On Nov. 15, 1979, he began anchoring a daily late-night special for ABC, "The Iran Crisis: America Held Hostage." The highly acclaimed program included a recapitulation of the day's general news report as well as late-breaking developments on Iran and the hostage situation. The program has been continued as "Nightline."

Mr. Reynolds also anchored ABC News' Special Reports. He was the man on the television screen who provided running commentary for the network's live coverage of the inauguration of President Reagan, the space shuttle launches and landings, and the assassination attempts against President Reagan and Pope John Paul II. Since 1968, he had covered all major political conventions for ABC.

"World News Tonight," with its three anchormen in widely separated cities, relies on the "mobile anchor" concept.

Mr. Reynolds demonstrated how this could work when he reported on the 1978 Camp David meetings that led to the accords between Israel and Egypt.

During the negotiations, he anchored the nightly newscast from Camp David itself and later from the White House.

Earlier, his work on President Nixon's historic first visit to China helped gain an Emmy Award for the network.

Over the years, Mr. Reynolds won some of broadcast journalism's most coveted awards. In 1969, he received the George Foster Peabody Award for his commentaries on world and national events and personalities. In 1980, he was awarded an Emmy for his reporting on ABC's "Post Election Special Edition."

He and "World News Tonight" coanchor Max Robinson recently received the Robert S. Ball Memorial Award from the Aviation and Space Writers Association for the ABC special called "The Next Step: Space Shuttle Columbia."

Among those who lauded Mr. Reynolds yesterday were his principal competitors. Dan Rather, the anchor of "CBS Evening News," said, "The Reynolds competition was always class all the way . . . If you were against Frank Reynolds, you knew that you were going to be beaten some of the time, but you would never be beaten unfairly."

Tom Brokaw of NBC News said Mr. Reynolds was "a kind of 24-hour-a-day newsman" who never lost "his sense of awe, his sense of delight at being where he was."

President Reagan said Mr. Reynolds "was one of America's foremost broadcast journalists, trusted and respected by millions of his fellow citizens, Nancy and I among them. To us he was also a warm, considerate friend who will be missed for his outstanding human qualities as well as for his many contributions as a newsman."

The Reagans and the Reynolds became friends during Reagan's unsuccessful campaign for the Republican presidential nomination in 1976. White House spokesman Larry Speakes said the Reagans were particularly fond of a piece Mr. Reynolds did on the air after Reagan lost out in the convention floor fight.

Despite his normal self-control, Mr. Reynolds allowed his emotions to show during the broadcast of the assassination attempt on Reagan in 1981. All three networks erroneously reported that presidential press secretary James Brady had been killed. In fact, Brady had been severely wounded. In the confusion surrounding the event, Mr. Reynolds was visibly angry that an incorrect report had been carried in the first place and that it seemed so difficult to find out the facts.

"When it turned out to be wrong, Frank Reynolds comes on and says to our reporters, 'Let's get it nailed down, somebody,' " Roone Arledge, president of ABC News, recalled several months after the incident. "He was justifiably angry, but everyone wrote that he lost control."

Mr. Reynolds was a native of East Chicago, Ind., and attended Wabash College in Indiana. He served in the Army during World War II and earned the Purple Heart Medal. He began his broadcast career in 1947 at station WJOB in Hammond, Ind. He spent 14 years as a newsman with Chicago television stations before joining ABC.

In 1965, he began a three-year stint as its White House correspondent. From May 1968, to December 1970, he and Howard K. Smith coanchored the "ABC Evening News." Mr. Reynolds lost the post to Harry Reasoner, who had moved to the network from CBS. He returned to the anchor slot eight years later.

Mr. Reynolds, who lived in Bethesda, was a member of the National Press Club, the Chicago Council on Foreign Relations, the White House Correspondents Association, the Radio-TV Correspondents Association, and Blessed Sacrament Catholic Church in Chevy Chase.

Survivors include his wife, the former Henrietta Mary Harpster, of Bethesda; five sons, Dean, James, John, Robert and Thomas; his mother, Helen Reynolds of Hammond, and three sisters, Nadyne Knight of East Chicago, Mary Frances Kilpatrick of Fort Lauderdale, Fla., and Terese Thanolt of Crown Point, Ind.