Electron acceleration by an intense electromagnetic wave incident obliquely to the ambient magnetic field in a plasma is considered. It is shown that the wave amplitude has a stochasticity inducing threshold. Although substantial acceleration can be achieved below this threshold, it is limited to the trapping width of a single resonance. Above threshold, the electrons can accelerate from resonance to resonance. It is also shown that when the parallel phase velocity of the electromagnetic waves is supraluminous, the Hamiltonian surfaces describing the wave–particle interaction are topologically open. In this case, electrons gain large amounts of energy. The mechanism is quite robust, being weakly sensitive to changes in the wave parameters and the electron’s initial energy; as a result, it is an ideal mechanism for space applications. As an application, the conditions are obtained for accelerating electrons to energies of several MeV using ground‐based transmitters.