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depmixS4 implements a general framework for defining and estimating dependent mixture models in the R programming language. This includes standard Markov models, latent/hidden Markov models, and latent class and finite mixture distribution models. The models can be fitted on mixed multivariate data with distributions from the glm family, the (logistic) multinomial, or the multivariate normal distribution. Other distributions can be added easily, and an example is provided with the exgaus distribution. Parameters are estimated by the expectation-maximization (EM) algorithm or, when (linear) constraints are imposed on the parameters, by direct numerical optimization with the Rsolnp or Rdonlp2 routines.