This work studies the theory of parametrically excited nonlinear systems in general, and its application in microelectromechanical systems (MEMS) in particular. A systematic approach is followed to discuss different sources of destabilization, ending up at nonlinear time-periodic systems. This should give a gentle introduction to the subject. Through the theoretical study presented, a novel idea for the MEMS industry is introduced, namely the broadband parametric amplification using a bimodal excitation method. This idea is then implemented in microsystems, by investigating a particular example, that is the microgyorscope. Given the low-cost of this device in comparison with other inertial sensors, it is being currently enhanced to reach a relatively higher sensitivity and accuracy. To this end, the theoretical findings, including the mentioned idea, are implemented in this device and prove to contribute effectively to its performance. Moreover, an experimental investigation is carried out on an analogous microsystem. Through the experimental study, an electronic system is introduced to apply the proposed bimodal parametric excitation method on the microsystem. By comparing the stability charts in theory and experiment, the theoretical model could be validated. In summary, a theoretical study is carried out through this work on parametrically excited nonlinear systems, then implemented on microgyroscopes, and finally experimentally validated. Thereby, this work puts a first milestone for the utilization of the proposed excitation method in the M/NEMS industry.