This package performs parametric and non-parametric estimation and simulation for multi-state discrete-time semi-Markov processes (Barbu et al., submitted). For the parametric estimation, several discrete distributions are considered for the sojourn times: Uniform, Geometric, Poisson, Discrete Weibull of type 1 and Negative Binomial. The non-parametric estimation concerns the sojourn time distributions, where no assumptions are done on the shape of distributions. Moreover, the estimation can be done on the basis of one or several sample paths, with or without censoring at the beginning or/and at the end of the sample paths. Estimation and simulation of discrete-time k-th order Markov chains are also considered. Semi-Markov models are specified by using the functions smmparametric() and smmnonparametric() for parametric and non-parametric specifications respectively. These functions return objects of S3 class (smm, smmparametric) and (smm, smmnonparametric) respectively (smm class inherits from S3 classes smmparametric or smmnonparametric). Thus, smm is like a wrapper class for semi-Markov model specifications. Based on a model specification (an object of class smm), it is possible to: • simulate one or several sequences with the method simulate.smm(); • plot conditional sojourn time distributions (method plot.smm()); • compute log-likelihood, AIC and BIC criteria (methods logLik(), AIC(), BIC()); • compute reliability, maintainability, availability, failure rates (methods reliability(), maintainability(), availability(), failureRate()). Estimations of parametric and non-parametric semi-Markov models can be done by using the function fitsmm(). This function returns an object of S3 class smmfit. The class smmfit inherits from classes (smm, smmparametric) or (smm, smmnonparametric). Based on a fitted/estimated semi-Markov model (an object of class smmfit), it is possible to: • simulate one or several sequences with the method simulate.smmfit(); • plot estimated conditional sojourn time distributions (method plot.smmfit()); • compute log-likelihood, AIC and BIC criteria (methods logLik(), AIC(), BIC()); • compute estimated reliability, maintainability, availability, failure rates and their confidence intervals (methods reliability(), maintainability(), availability(), failureRate()). The implemented methods are described in: • Barbu & Limnios (2008) • Barbu & Limnios (2006) • Trevezas & Limnios (2011)