The formal theory of the interaction of mildly relativistic electrons with a cyclotron resonant applied electromagnetic field described by geometric optics is developed. The electron distribution function is written as the sum of a quasi‐static partf0and a high frequency partf1. A quasi‐linear theory is employed to describe these. The resulting transport equationf0is written to lowest significant order jointly in the reciprocal of the gyration frequency and the bounce frequency. It includes a relativistic collision term and a drag term associated with synchrotron emission. The linearized equations forf1are solved, and an expression for the high‐frequency current is derived.