Charged particles in a uniform magnetized field respond both to Larmor and electric forces. The kinematic behavior for a smoothly varying electric force is simply determined and may generally be described as having gyrational motion superimposed upon a continuously evolving ‘‘guiding center’’ or drift motion. When the electric force is stochastic (i.e., the time scale over which the electric field changes is much shorter than the gyroperiod) but has stationary statistical properties, the kinematics are a variant of an Ornstein–Uhlenbeck process and the asymptotic behavior of the particle motion and the resulting Fokker–Planck solution can be exactly obtained. The random walk character of the particle trajectories results in drift velocities whose rms value is preserved while the rms gyration speed increases linearly with time, providing a relatively efficient mechanism for introducing thermal energy into an ensemble of particles. The stochastic behavior, therefore, is demonstrably nonadiabatic, and there are no ‘‘adiabatic invariants’’ describing the kinematics. An illustrative example where the electric force varies according to discontinuous instantaneous jumps with random orientation at random times is considered. This example represents a potential energization mechanism for space and laboratory plasmas.