The genetic structure, kinship and type of post-marital residence are studied in four native groups of the Gran Chaco, through the analysis of somatometric traits. The sample used was published by Lehmann-Nitsche (1907) and is represented by 158 individuals of both sexes. To meet the objectives, methods and techniques of multivariate statistics and population genetics of quantitative traits were applied. The results show a genetic divergence (FST) of 0.047, a greater kinship between chorote and mataco, a significant isolation of the chiriguano, an important interaction of the chorote with the rest of the groups, a greater regional mobility of males than of the women, and a matrilocal or bilocal post-marital residence system.