The problem of a particle trapped in a time‐dependent meridional magnetic mirror field and at the same time subjected to a time‐dependent perpendicular electric field(E·B = 0)is considered. Bounce‐averaged guiding‐center theory is used to derive expressions for the drift velocity conponents. These drift expressions depend in a straightforward fashion on the structures of the magnetic and electric fields and on the particle charge, kinetic energy, longitudinal invariant, and bounce period. In the special case of a static magnetic field, no electric field, andJ = 0particles, the drift equations are integrated and the bounce‐averaged guiding‐center trajectory obtained.