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The magnetoplasmon spectrum of two-dimensional electron gas systems with both Rashba and Dresselhaus spin-orbit interactions is investigated theoretically. The coexistence of the two types of spin-orbit interactions leads to resonant splittings of the collective excitation modes and makes the magnetoplasmon spectrum anisotropic with respect to the direction of the wave vector. The anticrossing gaps in the magnetoplasmon spectrum vary with the angle of the wave vector and reach their extrema at several fixed directions. Such anisotropic splittings could be used to evaluate the relative strength of the Rashba and Dresselhaus spin-orbit interactions in two-dimensional electron systems.