The paper deals with the propagation of a finite-amplitude circularly polarized electromagnetic plane wave through a fully ionized hot collisionless plasma, composed of Q (≧1) types of ions and of electrons, as a strict solution of the non-relativistic self-consistent Vlasov equations within the scope of some given applicability criterions. A constant magnetic field and a constant total plasma stream, both parallel to the wave propagation direction, are allowed. Wave propagation and particle motion are separately discussed. Particularly, the possible existence of an anomalous wave, propagating with light speed through multi-component (Q>1) plasmas with arbitrary ratios plasmafrequency/wavefrequency, and the possible existence of multi-component plasmas with temperatures, far below thermonuclear temperatures, but under electromagnetically generated fusion conditions, are proved. The treated solution is of physical and astrophysical interest, likewise.