Electrostatic micro-electro-mechanical system (MEMS) is a special branch with a wide range of applications in sensing and actuating devices in MEMS. In this paper the perturbation analysis of the electrostatically actuated MEMS resonant sensors which represented by a modified Duffing - Van der Pol equation subjected to weakly non-linear parametric and external excitations is studied by using a perturbation technique (multiple time scales). Harmonic resonance and subharmonic resonances of order (1/2 and 1/3) are investigated. For each resonances we obtain the modulation equations in the amplitude and phase, steady state solutions, frequency-response equations and stability conditions are determined. Effects of different parameters on the system behavior are investigated numerically. Results are presented graphically and discussion is provided.