  We examine linear and quasi-liner stages of Cherenkov-drift instability in
the relativistic magnetized electron-positron plasma. The external magnetic
field lines are assumed to be slightly curved. In this case the curvature drift
of relativistic beam particles plays decisive role in the development of the
instability. Quasi-linear relaxation of the relativistic beam leads to
diffusion of the resonant particles in the momenta space. The expressions for
diffusion coefficients of Cherenkov-drift instability are obtained.
