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This paper introduces the hhsmmR package, which involves functions for initializing, fitting, and predication of hidden hybrid Markov/semi-Markov models. These models are flexible models with both Markovian and semi-Markovian states, which are applied to situations where the model involves absorbing or macro-states. The left-to-right models and the models with series/parallel networks of states are two models with Markovian and semi-Markovian states. The hhsmm also includes Markov/semi-Markov switching regression model as well as the auto-regressive HHSMM, the nonparametric estimation of the emission distribution using penalized B-splines, prediction of future states and the residual useful lifetime estimation in the predict function. The commercial modular aero-propulsion system simulation (C-MAPSS) data-set is also included in the package, which is used for illustration of the application of the package features. The application of the hhsmm package to the analysis and prediction of the Spain's energy demand is also presented. [ABSTRACT FROM AUTHOR]