Fast electron acceleration and velocity diffusion are investigated in
wavepackets formed by large-amplitude waves with relativistic phase ve
locities. In tokamaks, such waves are generated, e.g. in current drive
by free-electron lasers where large-amplitude electron plasma waves o
r lower hybrid waves are generated. At small field intensities, the ve
locity diffusion in wavepackets with Gaussian-like envelopes is found
to be well described by the quasilinear approximation. At large field
intensities, trapping effects become important, and deviations from qu
asilinear diffusion are found. It is demonstrated that these deviation
s may have a significant effect on the velocity distribution of the el
ectrons. A wave-induced runaway-like phenomenon of relativistic electr
ons is discussed.