A generalized canonical analysis is considered in order to build a test statistic for the comparison of factor subspaces of k related populations. This test constitutes a generalization of a test of comparison of two factor subspaces (Dauxois, J., Romain, Y. and Viguier, S. (1993). Comparison of two factor subspaces. J. Multivariate Anal., 44, 160-178). A first stage of the generalization is made in the case of two populations, with the infinite dimension, and without the hypothesis of sphericity. A numerical example is given to compare the test statistics for k = 2, and another example illustrates the k-sample case.