RSOI on the magnetoplasmons of a modulated 2DEG. In the absence of RSOI but as a result of modulation, Weiss[14–16] oscillations in the magnetoplasmon spectrum appear[17]. These oscillations are due to the commensurability of two characteristic length scales of the system: the cyclotron diameter at the Fermi level and the period of the electric modulation. Weiss oscillations are distinctly different from the Shubnikov-de Hass (SdH)[18] oscillations that appear at higher magnetic field strengths. The period of Weiss oscillations depends on both the modulation period and the square root of the number density of the 2DEG, in contrast to the linear dependence on the number density of the SdH oscillations. Moreover, the amplitude of Weiss oscillations is weakly affected by temperature as compared to SdH oscillations. Theoretical study of RSOI effects on single particle quantum transport in a modulated 2DEG was recently carried out[19], where modulation leads to the broadening of the levels of two unequally spaced branches into bands whose widths oscillate as a function of magnetic field. Furthermore, recently RSOI effects on magnetoplasmon excitations with- out modulation have been addressed[13] but RSOI effects on commensurability oscillations in magnetoplasmons of a M2DEG have not been discussed so far. This is the subject of the present paper. The present work examines RSOI effects on the collective excitations (magnetoplasmons) of a modulated 2DEG. This investigation is performed within the self- consistent-field approach at finite temperature. We analyze the dynamic, nonlocal dielectric function of the system and highlight the modulation-induced effects on the intra-Landau band magnetoplasmon spectrum in the presence of RSOI. In addition, our finite tempera- ture theory facilitates analysis of effects of temperature on the magnetoplasmon spectrum of a M2DEG in the presence of RSOI as there is an apparent gap in the literature[17] re- garding finite temperature effects on the magnetoplasmon spectrum of a M2DEG even in the absence of RSOI. We expect experimental studies such as in-elastic light scattering[20] and spectroscopic[21] measurements of magnetoplasmons spectrum of a modulated system in the presence of RSOI would allow verification of the model presented here and would be quite revealing as they pertain to spin-orbit interaction effects on the many-body properties of a 2DEG. 3