Elliptically polarized intense electromagnetic waves, under certain conditions, undergo self-precession (frequency rho-dot) and shift in wave frequency (delta..omega..) due to nonlinear interaction in the magnetized gaseous plasma background. Assuming a classical model of the neutral atom, embedded in the magnetized plasma, the nonlinear distortion of stationary electron orbit is calculated, and the resulting nonlinear polarization is shown to be dependent on intensity-induced nonlinear effects rho-dot and delta..omega.. of the strong radiation due to magnetized plasma background. The consequent nonlinear increment in kinetic energy, angular momentum of the bound electron, and consequent induced magnetization have been derived. For interaction of ruby laser (power flux approx. 10 MW/cm/sup 2/, lambda=6943 A) in the magnetized (H/sub 0/ approx. 10/sup 2/ gauss) hydrogen plasma (N approx. 10/sup 12//cm/sup 3/) background, rho-dot and delta..omega.. are not very large in nonresonant interactions but are likely to be enhanced in some phase-matching and resonant interactions. The possibility of detection of depending on rho-dot and delta..omega.. has been discussed. A brief qualitative study is given for the multiphoton excitation of neutral atoms and Zeeman splitting of the spectral lines.