The regime switching models are particularly popular in the comity of non-linear models; it is of interest to investigate regime switching models with GARCH specification. GARCH model was augmented with STAR model vis-a vis Exponential autoregressive GARCH (EAR-GARCH), Exponential smooth transition autoregressive GARCH (ESTAR- GARCH) model and Logistic smooth transition autoregressive GARCH (LSTAR-GARCH) model. The properties of the new models were derived and compared with conventional GARCH model which shows that the variance obtained for STAR-GARCH model was minimum compared to classical GARCH model, the new methodology proposed is illustrated with foreign exchange rate data from Great Britain (Pound) and Botswana (Pula) against United States of America (Dollar). It is evident that all STAR-GARCH outperformed the classical GARCH model, however, LSTAR-GARCH performed best and closely followed by ESTAR-GARCH, this is followed by EAR-GARCH. The implication is that the use of LSTAR –GARCH produces the best result; however LSTAR may be utilized in some occasions.