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It is shown that in the general case the conditions of cyclotron resonances should be formulated with regard to the influence of intense electromagnetic fields, if present, on the particle motion. Moreover, the greater is the wave field strength, the more significantly such effects are pronounced. These effects lead to the appearance of qualitatively new features in the particle dynamics. Such features include regularization of the particle dynamics, particularly a stepwise structure appears in the time dependencies of momenta and energy. The second feature concerns a new generation mechanism of regimes with dynamical chaos. This mechanism differs from the known mechanisms that arise as a result of the intersection of homoclinic structures. The new mechanism appears when particle trajectories pass the point associated with the singular solution of the equations under consideration (at the points of such solutions, the uniqueness theorem is violated).