Asthma and chronic obstructive pulmonary disease (COPD) can be confused in clinical diagnosis due to overlapping symptoms. The purpose of this study is to develop a method based on multivariate pulmonary sounds analysis for differential diagnosis of the two diseases. The recorded 14-channel pulmonary sound data are mathematically modeled using multivariate (or, vector) autoregressive (VAR) model, and the model parameters are fed to the classifier. Separate classifiers are assumed for each of the six sub-phases of flow cycle, namely, early/mid/late inspiration and expiration, and the six decisions are combined to reach the final decision. Parameter classification is performed in the Bayesian framework with the assumption of Gaussian mixture model (GMM) for the likelihoods, and the six sub-phase decisions are combined by voting, where the weights are learned by a linear support vector machine (SVM) classifier. Fifty subjects are incorporated in the study, 30 being diagnosed with asthma and 20 with COPD. The highest accuracy of the classifier is 98 percent, corresponding to correct classification rates of 100 and 95 percent for asthma and COPD, respectively. The prominent sub-phase to differentiate between the two diseases is found to be mid-inspiration.