This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspeci cation. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The rst-stage nonparametric estimation may depend on nite dimensional parameters. We characterize: (1) conditions under which the rststage estimation of nonparametric components do not a ect the asymptotic distribution, (2) conditions under which the asymptotic distribution is a ected by the derivatives of the rst-stage nonparametric estimator with respect to the nite-dimensional parameters, and (3) conditions under which one can allow non-smooth objective functions. Our framework is illustrated by applying it to three examples: (1) pro led estimation of a single index quantile regression model, (2) semiparametric least squares estimation under model misspeci cation, and (3) a smoothed matching estimator.