To provide ball screw parts which have long life against rolling fatigue and high crack strength and in which an increase in the ratio of dimensional change with the lapse of time is suppressed and also to provide a ball screw.

For the ball screw parts, after the steel is subjected to carbonitriding treatment at a carbonitriding treatment temperature higher than the A1 transformation point, it is cooled to a temperature lower than the A1 transformation point, reheated to a hardening temperature not lower than the A1 transformation point and lower than the carbonitriding treatment temperature, and then quenching is applied.