For the single-drive Mach-Zehnder electrooptical modulator applied in radio over fiber (RoF) and sub-carrier multiplexing systems, the situation for two radio frequency signals inputs is discussed and an exact analytical solution for arbitrary order inter-modulation distortion (IMD) and harmonic terms is derived. The correctness of the analytical solution is approved by numerical results. Analytical results indicate that the third-order IMD is independent of the offset phase shift of the modulator and is only dependent on the modulation index of RF signals. In addition, when the applied offset voltage equals the half-wave voltage of the modulator, there are only even-order distortion terms. With the presented analytical expression, it is convenient to design the analog optical communication systems, precisely predict the nonlinear characteristics of the external modulator and optimize the system's performance.