In France, beef traits of artificial insemination (AI) beef bulls are improved through the sequential selection for their own performances and for their male progeny performances, both being recorded in test stations. The efficiency of such programmes mainly depends on the genetic correlations between sire performances and progeny beef traits. Such correlations were independently estimated, using the multivariate REML (restricted maximum likelihood) method in a Limousin and a Charolais programme. In both breeds, high genetic correlations were observed between sires and progeny analogous morphology scores (from 0.64 to 0.82). Genetic correlations estimated between sires and progeny growth (from 0.41 to 0.70) were lower probably due to the difference of diet in central and progeny stations. Correlations between sire muscling scores and progeny skeletal frames (and vice-versa) were negative (from -0.05 to -0.58). The genetic correlations of sire traits with progeny dressing percentage (DPp) and carcass fatness score (CFp) were only low to moderate. These results show that the selection of bulls at the end of performance testing in test stations may be efficient in improving progeny growth and morphology. However, such a selection is insufficient in improving their dressing percentage and carcass composition.