​​Joseph Ngatchou-Wandjil: Abstract - We study some general methods for testing the goodness-of-fit of a general nonstationary and dependent nonlinear time series model.  Our tests are based on some marked empirical processes that we show to converge in distribution to a zero-mean Gaussian process.  We investigate the behavior of these processes under a sequence of local alternatives.  Our results are applied to testing a general class of nonlinear semiparametric time series models.  A simulation​experiment shows that the Cram​ér-Mises test studied behaves well on the examples considered.