<p>An electric power-steering device has a speed-reducing mechanism (17) for reducing the speed of an output shaft (16) of an electric motor (15). The speed-reducing mechanism (17) has an internal gear (39) engaged and rotated with the output shaft (16) and an external gear (40) with which the internal gear (39) internally meshes. A drive pulley (41) rotatable together with the external gear (40) and a driven pulley (42) provided so as to surround a steering shaft are connected by an endless belt (43). Speed reduction is obtained by the internal gear (39) and the external gear (40), and the speed-reducing mechanism (17) as a whole achieves a high reduction ratio without greatly reducing the diameter of the drive pulley (41).</p>