Nanoelectromechanical systems (NEMS) have drawn considerable attention towards several sensing applications such as force, spin, charge and mass. These devices due to their smaller size, operate at very high frequencies (MHz - GHz) and have very high quality factors (102 -105). However, the early onset of nonlinearity limits the linear dynamic range of these devices. In this work we investigate the nonlinearities and their effect on the performance of graphene based NEMS. Electromechanical devices based on 2D materials are extremely sensitive to strain. We studied the effect of strain on the performance of single layer Graphene NEMS and show how the strain in Graphene NEMS can be tuned to increase the range of linear operation. Electromechanical properties of the doubly clamped graphene resonators deviates from the flat rectangular plate as the former possesses geometrical imperfections which are sometimes orders of magnitude larger than the thickness of the resonator. Due to these imperfections we report an initial softening behavior, turning to strong hardening nonlinearity for larger vibration amplitude in the back-bone curve. We have also studied the frequency stability of graphene resonators. Frequency stability analysis indicates departure from the nominal frequency of the resonator with time. We have used Allan Variance as a tool to characterize the frequency stability of the device. Frequency stability of graphene resonator is studied in an open loop configuration as a function of temperature and bias voltage. The thesis concludes with a remark on the future work that can be carried out based on the present studies.