This Monograph provides Bayesian Methodology for Structural Change problems through Changes in Parameters of the models and Structural Changes through Mixture of Models in Time series Analysis. It also deals the models with auto correlated errors and derived the Bayesian solutions. A computer simulation study was carried out. The main aims of the numerical study are (i) to illustrate the evaluation of the estimates of the parameters on the basis of the methodology developed and (ii) to compare the two different methodologies developed based on the estimates.