Finite mixture of models based on the proportional hazards or the accelerated failure time assumption lead to a large variety of lifetime regression models. We present several iterative methods based on EM and Stochastic EM methodologies, that allow fitting parametric or semiparametric mixture of lifetime regression models for randomly right censored lifetime data including covariates. Their identifiability is briefly discussed and in the semiparametric case we show that simulating the missing data coming from the mixture allows to use the ordinary partial likelihood inference method in an EM algorithm's M-step. The effectiveness of the new proposed algorithms is illustrated through simulation studies.