An object is to reduce various losses occurring in a speed-reduction/differential gear apparatus for electric vehicles including a planetary-gear speed reducer and a differential device, thereby improving transmission efficiency of the driving force and increasing travel distance of the electric vehicle per battery charge. A speed-reduction/differential gear apparatus for electric vehicles includes a planetary-gear speed reducer and a differential device. A planetary gear mechanism in the speed reducer includes a speed-reducer-side carrier which has its inner diameter surface supported by a speed-reducer-side carrier support bearing. The invention provides proper mesh between in the pair of engaging teeth, leading to decrease in loss torque.