We analyze an electron-hole asymmetry model for simultaneous two-state operation in semiconductor quantum dot lasers. From the linearized equations, we determine simple analytical expressions for the relaxation oscillation (RO) frequencies. Of particular interest is the fact that different expressions for the RO frequencies are obtained depending on the relative values of the photon lifetime and the basic time scale of the nonlinear intradot interaction. If comparable, we find only one frequency that depends on a combination of the two-state intensities.