Modeling is described for the simultaneous analysis of two-level data in several populations. A typical example is cluster sampling of students within schools, where schools of different types are represented, eg public and private schools. Multivariate measurements on each student are assumed to give rise to a latent variable model. Of interest is to study across-population differences and similarities with respect to the within- and between-group covariance matrices and with respect to the mean vector. The methodology is illustrated by a comparative analysis of achievement structures in Catholic and public schools.