A rotary piezoelectric motor (1) in which a geometrical asymmetry can be introduced, e.g. in the counter-masses (11, 14) or in the stator fixing elements (10), in order to produce a phase shift previously obtained using a phase quadrature power supply. A simplified single-phase power supply (40) can be used with one such motor. The inventive motors offer advantages in terms of cost and reliability, particularly for motors that require only a single direction of rotation. The motors are particularly suitable for small motors such as those used for clock and watch making, microsurgery or microelectronics.