Eight months before the first primary balloting, the Republican Presidential campaign of Lamar Alexander announced plans today for a television advertising drive in the pivotal states of Iowa and New Hampshire.

Worried, perhaps, that Mr. Alexander is still a stranger in those states despite repeated visits, the candidate's advisers are hoping that the commercials make him a known quantity. The advertisements will also be a way for him to try to keep from being overshadowed by a more recent, better known entrant who, like Mr. Alexander, casts himself as a Washington outsider, Gov. Pete Wilson of California.

The nearly identical 60-second Alexander commercials, which will continue until mid-August, offer an introduction to the candidate, with emphasis on his service as Governor of Tennessee. Campaign officials said they had budgeted $300,000 for the advertising drive, which will also include some radio spots.

The commercials are the latest demonstration of how the compressed schedule of primaries and caucuses next year is leading campaigns to move up timetables on everything.