Provided are an electric power steering system and a vehicle steering system each including rack-and-pinion mechanisms (14A, 14B). A rack shaft (3) has a first rack (7A) and a second rack (7B) that are formed on the axially opposite sides of the axial center of the rack shaft (3). The first rack (7A) has a regular pitch p between rack teeth, the second rack (7B) has a regular pitch p between rack teeth, and these pitches p are equal to each other. A predetermined difference is set between the phase of gear teeth engagement between a first pinion shaft (8A) and the first rack (7A), which constitute the first rack-and-pinion mechanism (14A), and the phase of gear teeth engagement between a second pinion shaft (8B) and the second rack (7B), which constitute the second rack-and-pinion mechanism (14B).