The pricing of Bermudan options amounts to solving a dynamic programming principle , in which the main difficulty, especially in large dimension, comes from the computation of the conditional expectation involved in the continuation value. These conditional expectations are classically computed by regression techniques on a finite dimensional vector space. In this work, we study neural networks approximation of conditional expectations. We prove the convergence of the well-known Longstaff and Schwartz algorithm when the standard least-square regression is replaced by a neural network approximation.