  We study McKean-Vlasov equations where the coefficients are locally Lipschitz
continuous. We prove the strong well-posedness and a propagation of chaos
property in this framework. These questions can be treated with classical
arguments under the assumptions that the coefficients are globally Lipschitz
continuous. In the locally Lipschitz case, we use truncation arguments and
Osgood's lemma instead of Gr\"onwall's lemma. This approach entails technical
difficulties in the proofs, in particular for the existence of solution of the
McKean-Vlasov equations that are considered. This proof relies on a Picard
iteration scheme that is not guaranteed to converge in an $L^1-$sense because
the coefficients are not Lipschitz continuous. However, we still manage to
prove its convergence in distribution, and the (strong) well-posedness of the
equation using a generalization of Yamada and Watanabe results.
