Robert E. Mulholland was promoted yesterday from president of the NBC television network to the new position of president and chief operating officer of the National Broadcasting Company. Grant A. Tinker, who made the announcement over closed-circuit TV to NBC affiliates joined the company recently as chairman and chief executive officer. He replaced Fred Silverman, who held the titles of president and chief executive officer.

Tinker attempted to explain the new distribution of titles and duties. Since Tinker's background is in programming (he was formerly head of MTM Enterprises, the company named for his ex-wife, Mary Tyler Moore) he said that Mulholland, 49, would concentrate on "broadcasting and business."

This arrangement, Tinker said, will "permit a team -- chairman and president -- who would complement, not duplicate, each other." The team's first order of business is wresting the television network from its long-held position at the bottom of the ratings with the skimpiest profits of the three networks.

Mulholland was named network president in 1977 by former NBC chief Herbert S. Schlosser, now an RCA executive. Before that, Mulholland was an executive vice president with NBC News for three years.

Replacing Mulholland as president of the television network will be Raymond J. Timothy, who was named executive vice president for affiliate relations at the same time Mulholland got the network presidency. Timothy, 48, "knows the station business inside-out," Tinker said in his announcement, adding, "Mulholland and Timothy in key new roles in one fell swoop: Not a bad day's work. I will not be the first to call them Bob and Ray."

The promotion for Mulholland raised speculation about his working relationship with William J. Small, president of NBC News. An NBC insider confirmed yesterday that the two men are said to "speak disparagingly of each other," but an NBC News spokesman said, "It's not true. They do get along, and they've known each other for 15 years."

One casualty of the change, though, is Mulholland's wife, Adrienne Cowles, who had been a documentary producer ("American Fashion: Rags and Riches") under Small. Yesterday, when her husband became Small's boss, she resigned.