An engine starter apparatus being arranged such that a rotational force from an electric motor (2) is transmitted to an output rotary shaft through a planetary speed reduction gear(7). The number Zs of teeth of a sun gear(4), the number Zp of teeth of a planet gear (7), the number Zi of teeth of an internal gear (6) and the number N of the planet gears satisfy the equation (Zs + Zi)/N an integer, and the pressure angle alpha bi of the engagement between the planet gear and the internal gear is arranged to be cos<-><1>{(Zi - Zp)/(Zs + Zp) x cos alpha bs}, where alpha bs is the pressure angle of the engagement between the sun gear and the planet gear.
