Optical frequency combs have resulted in significant advances in optical frequency metrology and found wide application to precise physical measurements and molecular fingerprinting. A direct analogue of frequency combs in the phononic or acoustic domain has not been reported to date. This thesis describes a series of results to provide the first clear evidence for the generation of phononic frequency combs in the domain of micromechanical resonators. These results are supported by a theoretical framework which was originally developed to predict the existence of such features of combs in physical systems described by Fermi-Pasta-Ulam dynamics. The phononic frequency combs is mediated by nonlinear coupling between a primary driven mode and one or more parametrically excited internal modes. We provide experimental evidence for the formation of such phononic frequency combs in systems comprising of 2 or more coupled modes, with results qualitatively consistent with previous numerical studies based on Fermi-Pasta-Ulam dynamics. Additionally, externally pumped comb processes are also reported. Through systematic experiments at different drive frequencies and amplitudes, we portray the well-connected processes of phononic frequency comb formation and define attributes to control their concomitant features. Further, the interplay between these new nonlinear resonances and the well-established Duffing phenomenon is also discussed. While the experimental verification of the existence of phononic frequency combs is of scientific interest, several potential engineering applications exist including the unique capability to track resonant frequency of a micromechanical resonator without the requirement for an external feedback loop to sustain oscillations at the resonant frequency. The initial experimental results also demonstrate that good short-term frequency stability may be obtained for such micromechanical resonators operated under ambient conditions.