A small relative population of high energy electrons has been predicted to have important beneficial effects on tokamak plasmas. In particular, the efficiency of steady state RF current drive can be increased and the high beta second regime of stable operation can be achieved. Formation of suitable concentrations of relativistic electrons using electron cyclotron heating (ECH) can be adversely affected by the occurrence of relativistic heating gaps, i.e. electron energy intervals within which the relativistic reduction of the electron gyrofrequency prevents resonance with the applied microwave heating power. A fully relativistic one-dimensional Fokker-Planck model of ECH exhibits efficient generation of relativistic electrons in typical tokamak plasmas for suitably chosen spectra of propagation vector,,and frequency, ω, of the ECH waves. Narrow illumination patterns, symmetric about normal incidence, can readily yield 10% relative densities of relativistic electrons when three or more frequencies are used. On the other hand, oblique illumination or broad illumination patterns with angular half-widths of 45° can give similar results when a single frequency is used.