According to character designer Takaya Imamura, each of the original Star Fox team members were modeled after his fellow Nintendo staff members at the time:

•Fox was based on Shigeru Miyamoto, with Miyamoto said to have a fox-like face.
•Falco was based on Tsuyoshi Watanabe, as the development team laughed over how his nose stuck out like a beak.
•Peppy was based on Katsuya Eguchi, with Eguchi said to have a mouth like a hare.
•Slippy was based on Yoichi Yamada, with Yamada said to have large, round eyes.

Imamura has also stated that he based Andross on his "boss at the time". It remains unknown who at Nintendo he is specifically talking about, though it's been long rumored that Andross was intended as a caricature of then-Nintendo president Hiroshi Yamauchi, who was known for his cutthroat and ruthless ways. However, it's also been speculated that Imamura is referring to Hiroshi Ikeda, the then-manager of Nintendo R&D4 (later EAD) who was also Miyamoto's boss, though it's worth pointing out that Ikeda had stepped down from his position in 1992.