Young rabbits, the dams of which came from a full diallel cross among four maternal lines (A, V, H and LP) and the sires from a single paternal line (R), that produce sixteen genetic groups, was carried out to evaluate the genetic groups and to estimate the crossbreeding genetic parameters of meat quality. The meat quality traits were recorded by NIRS from a sample of 285 longissimus lumborum muscles. Crossbreeding parameters were estimated according to Dickerson model. No differences in protein were found. The line A had significant differences with V line for intramuscular fat, and fatty acids groups. Significant differences for these traits appeared between the crossbred AH and VV (in favor of AH). As conclusion, the significant contrasts between genetic types for chemical composition of the meat are mainly consequence of direct-maternal genetic effects, having grandmaternal and maternal heterosis effects a less relevant role.