Employing a two-parameter model for representing the radiation field, the theory of cosmic-ray acceleration by cyclotron autoresonance is analytically generalized here to include any state of polarization. The equations are derived rigorously and used to investigate the dynamics of the nuclides 1H 1 , 2He 4 , 26Fe 56 , and 28Ni 62 , in severe astrophysical conditions. Single-particle calculations and many-particle simulations show that these nuclides can reach ZeV energies (1 ZeV = 10 21 eV) due to interaction with superintense radiation of wavelengths λ = 1 and 10 µm, and λ = 50 pm, and magnetic fields of strengths at the mega-and gigatesla levels. Examples employing radiation intensities in the range 10 32 − 10 42 W/m 2 are discussed.