Model-based clustering is a powerful technique for discovering natural groupings within a wide array of data. Model-based clustering typically involves the development of a family of mixture models and the imposition of these models upon data: the resulting parameter estimates then give estimates of group membership. This thesis focuses on extending the mixtures of multivariate ' t'-factor analyzers model to include constraints on the degrees of freedom parameter and the error variance matrix. The result is a family of four mixture models. Parameter estimates for this family of models are computed using the alternating expectation-conditional maximization algorithm and convergence is determined based on Aitken's acceleration. Model selection is carried out using the Bayesian information criterion and the integrated completed likelihood. This novel family of four mixture models is then applied to simulated and real data where clustering performance exceeds that of established model-based clustering methods.