Abstract. The spectrum and damping factor of plasma and magnetoplasma waves in a two-dimensional electron gas at low temperatures on the Graphene are calculated, taking into account local electron states at impurity atoms. It is shown that localization of electrons decreases the frequency of long-wave plasmons and rear ranges the magnetoplasma spectrum in the vicinity of resonant frequencies of electron transitions between the Landau levels and local levels. As a result, the plasma absorption peak is displaced towards low frequencies, and the magnetoplasma peak splits. The characteristics of plasmons and magnetoplasmons are calculated for parameters on the Graphene at the boundary between silicon and silicon dioxide.