Economic and finance time series are typically asymmetric and are expected to be modeled using asymmetrical nonlinear time series models. Smooth Transition Autoregressive (STAR) models: Logistic (LSTAR) and Exponential (ESTAR) are known to be asymmetric and symmetric respectively. Under non-normal and heteroscedastic innovations, the residuals of these models are estimated using Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models with variants which include linear and nonlinear forms. The small sample properties of STAR-GARCH variants are yet to be established but these properties are investigated using Monte Carlo (MC) simulation. An MC investigation was conducted to investigate the performance of selections of STAR-GARCH models by classical nonlinear selection approaches. The ARCH(1) and GARCH(1,1) models were the linear GARCH specifications while the Logistic Smooth Transition-ARCH (LST-ARCH(1,1)), Logistic Smooth Transition- GARCH (LST-GARCH(1,1)) and Asymmetric Nonlinear Smooth Transition-GARCH (ANST-GARCH(1,1)) models were the nonlinear GARCH specifications. The nonlinearity parameter in the variance equations and Autoregressive (AR) parameters were varied along with different sample sizes. With the assumption of normality, the results showed that the selection of LSTAR models were actually affected by the structure of the innovations and this improved as sample size increased. Misspecification tests showed that these models cannot be misrepresented in the real sense.