This chapter presents Bayesian inferences for general continuous time Markov chains (CTMC). Limiting and stationary distributions for continuous time Markov chains are determined in much the same way as that for discrete time Markov chains. Similar to the discrete case, time reversibility is the last major concept to be defined for CTMC. The three phases of Bayesian inference will be presented for the Kimura model of molecular evolution. Then the null hypothesis supports the Felsenstein-Churchill process, and in order to illustrate Bayesian inferences, holding time data will be generated that favor the alternative hypothesis, the Hasegawa, Kishino, Yano model. The chapter introduces the continuous time version of epidemic models. Bayesian inferences for continuous type Markov chains has been an active area of research and the following references should be appealing to the student who wants to contribute to the literature on the subject.