Comment: 44 pages, 4 figuresThe goal of this paper is to extend the method of estimating Impluse Response Functions (IRFs) by means of Local Projection (LP) in a nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for a Markov process, and explain how their Impulse Response Functions are directly linked to the nonlinear Local Projection, as in the case for the linear setting. We then present a nonparametric LP estimator, and compare its asymptotic properties to that of IRFs obtained through direct estimation. We also explore issues of identification for the nonlinear IRF in the multivariate framework, which remarkably differs in comparison to the Gaussian linear case. In particular, we show that identification is conditional on the uniqueness of deconvolution. Then, we consider IRF and LP in augmented Markov models.