In this paper we present a general multivariate approach to the analysis of functional imaging studies. This analysis uses standard multivariate techniques to make statistical inferences about activation effects and to describe the important features of these effects. More specifically, the proposed analysis uses multivariate analysis of covariance (ManCova) with Wilk's lambda to test for specific effects of interest (e.g., differences among activation conditions), and canonical variates analysis (CVA) to characterize differential responses in terms of distributed brain systems. The data are subject to ManCova after transformation using their principal components or eigenimages. After significance of the activation effect has been assessed, underlying changes are described in terms of canonical images. Canonical images are like eigenimages but take explicit account of the effects of error or noise. The generality of this approach is assured by the general linear model used in the ManCova. The design and inferences sought are embodied in the design matrix and can, in principle, accommodate most parametric statistical analyses. This multivariate analysis may provide a statistical approach to PET activation studies that 1) complements univariate approaches like statistical parametric mapping, and 2) may facilitate the extension of existing multivariate techniques, like the scaled subprofile model and eigenimage analysis, to include hypothesis testing and statistical inference.