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ln this dissertation, we present Bayesian alteniatives for classification probiem under different approaches. First of all, we propose a Box and Cox transformation to have normal data to be used in classification problems. We also consider the classification problem assuming a vector X with a mixture of inultivariate normal distributions, using Bayesian procedures to buiid a classification rule. We also consider the classification for binary data and correlated binary data using the Bayesian approach and also introducing randoin effects to capturate the correlation. For the Bayesian approach, we use MCMC methods and we consider the utilization of the software "Ox' as a great altemative for probiems related the efficiency of the algorithm.