A First Showing for 'Star Trek' Pilot (Published 1986)

''The Cage,'' the first pilot episode made in 1964 for the television series ''Star Trek,'' will be shown beginning Aug. 7 at the Museum of Broadcasting, 1 East 53d Street. The episode, made in black and white, featured Jeffrey Hunter in the role of Captain Pike, commander of the starship Enterprise.

It was written by Gene Roddenberry, creator of the television series, and has never been shown publicly in its entirety.

The episode, which also starred Leonard Nimoy as Mr. Spock, was initially rejected by WNBC-TV. In 1965, at the request of the network, a second pilot show, called ''Where No Man Has Gone Before,'' was made. Mr. Hunter was unavailable to repeat his role and William Shatner was cast as Captain Kirk. The series, which has been referred to as a space western by its creator, was then accepted by the network.

Although the episode was never shown, the story behind ''The Cage'' was later incorporated into a two-part ''Star Trek'' episode called ''The Menagerie.''

On the first day of the screenings, a special seminar with Mr. Roddenberry is planned. The screening, which runs for 65 minutes, will begin at 5:30 P.M., followed by the discussion. Advance tickets are $7.

The episode, which is expected to be available on home video in the fall, will be shown daily through Sept. 18. Museum hours are noon to 5 P.M. Wednesday through Saturday and noon to 8 P.M. on Tuesday. Admission is $3 ($2.50 for students and $1.50 for the elderly and those under 13.) Information: 752-7684.