Abstract. Patterns of genetic variation and covariation strongly affect the rate and direction of evolutionary change by limiting the amount and form of genetic variation available to natural selection. We studied evolution of morphological variance-covariance structure among seven populations of house finches (Carpodacus mexicanus) with a known phylogenetic history. We examined the relationship between within-and among-population covariance structure and, in particular, tested the concordance between hierarchical changes in morphological variance-covariance structure and phylogenetic history of this species. We found that among-population morphological divergence in either males or females did not follow the within-population covariance patterns. Hierarchical patterns of similarity in morphological covariance matrices were not congruent with a priori defined historical pattern of population divergence. Both of these results point to the lack of proportionality in morphological covariance structure of finch populations, suggesting that random drift alone is unlikely to account for observed divergence. Furthermore, drift alone cannot explain the sex differences in within-and among-population covariance patterns or sex-specific patterns of evolution of covariance structure. Our results suggest that extensive among-population variation in sexual dimorphism in morphological covariance structure was produced by population differences in local selection pressures acting on each sex.Key words. Carpodacus mexicanus, genetic correlation, phenotypic covariance, sexual size dimorphism.Received November 1, 1999. Accepted April 2, 2000.Patterns of genetic variation and covariation strongly affect the rate and direction of evolutionary change (Lande 1976(Lande , 1980Lande and Arnold 1983). Although genetic variancecovariance structure (hereafter covariance structure) that results from developmental or functional interrelationships among traits may be adaptive when it is formed (Berg 1960;Cheverud 1984;Wagner 1988), it can bias evolutionary change in response to new environments (e.g., Maynard Smith et al. 1985;Arnold 1992).Two issues related to covariance structure of populations are of a particular interest to studies of evolution: the relative temporal constancy of genetic covariances and the relationship between phenotypic and genetic covariance structures (Lande 1980(Lande , 1985Turelli 1988). Genetic covariance structure may remain constant during the initial periods of taxa divergence, but eventually it is expected to evolve under selection or drift (e.g., Lande 1980Lande , 1985Zeng 1988;Schluter 1996). Indeed, theoretical and empirical studies have suggested that genetic correlations can strongly bias short-term evolution, but their importance should diminish over time (Cheverud 1984;Lofsvold 1986Lofsvold , 1988Turelli 1988;Zeng 1988;Shaw et al. 1995;Schluter 1996) especially when the correlations themselves are the subject of selection (e.g., Berg 1960; Wilkinson et al. 1990), and constancy of genetic covariance patte...