The composer of both Pikmin and Pikmin 2's music is Hajime Wakai.
The music in Pikmin
Every area has a very different musical theme. The music changes depending on the time of day.
Strawberry Flower released a Pikmin-themed song, Ai No Uta, along with the release of Pikmin.
The music in Pikmin 2
Pikmin 2 features distinctive music in both the overworld and the caves. It changes when Pikmin interfere with beasts or when they carry a treasure. This is most easily noticed in the minimalistic music pieces playing in the caves. The cave music appears to be chosen according to the difficulty and kind of hazards/beasts that await the Pikmin. In rest areas, a recognizable soft melody plays. Above ground, the music also changes depending on the time of the day, much like in the first Pikmin game.
For the ads of Pikmin 2, another song from Strawberry Flower, Tane no Uta, was used.