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The two-dimensional cubic nonlinear SchrSdinger (NLS) equation is a model for the evolution of two-dimensional nearly monochromatic gravity-capillary waves that are slowly modulated in deep water.All nontrivial-phase solutions of the NLS equation are known to be unstable.The NLS equation is derived from the Euler equations via a perturbation analysis.If this perturbation analysis is taken one order further, the modified nonlinear Schr(o)dinger (MNLS) equation is obtained.We establish that nontrivial-phase solutions of the MNLS equation are unstable.We compare the NLS and MNLS models by examining the growth rates of the instabilities of solutions to these equations.This is joint work with Eddie Feeley.