Parametrically excited systems are not uncommon in the many structures and systems built today. Classical analysis shows that the presence of viscous damping in a linear system does not limit the infinite amplitude of the parametric resonance. In this paper we investigate the role of damping in the suppression of both fundamental and principal parametric resonances in nonlinear systems. The results show that critical values of damping are required to suppress a parametric resonance. In some cases, the nonlinearity causes a multivalued response that allows nontrivial responses to exist at levels of damping that exceed the critical threshold of damping for stability predicted by linear theory. For small values of damping, chaotic responses were observed.