Suppose that data are collected fromkindependent but closely related populations and that a canonical correlation analysis is to be performed within each group. In such a situation, it may turn out that the transformation to canonical variates is similar across allkgroups. The common canonical variates model studied in this article assumes that the transformation to canonical variates is actually identical across groups, while the canonical correlations may vary. We develop some algebra of the common canonical variates model, discuss normal theory maximum likelihood estimation and likelihood ratio testing give illustrative examples.