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In this paper the existence of a smooth density is proved for the solution ofan SDE, with locally Lipschitz coefficients and semi-monotone drift, underH\"ormander condition. We prove the nondegeneracy condition for the solution ofthe SDE, from it an integration by parts formula would result in the Wienerspace. To this end we construct a sequence of SDEs with globally Lipschitzcoefficients whose solutions converge to the original one and use some Lyapunovfunctions to show the uniformly boundedness of the p-moments of the solutionsand their Malliavin derivatives.

Smooth density for the Solution of Scalar SDEs with Locally Lipschitz Coefficients under H\"ormander Condition