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[EN] The aim of this study was to estimate the genetic and environmental parameters and crossbreeding effects on fatty acid and fat traits in the Iberian pig. Our final goal is to explore target selection traits and define crossbreeding strategies. The phenotypes were obtained under intensive management from 470 animals in a diallelic experiment involving Retinto, Torbiscal, and Entrepelado lines. The data set was composed of backfat thickness at the fourth rib (BFT), intramuscular fat (IMF) in the longissimus thoracis (LT), and the fatty acid profile for IMF and subcutaneous fat (SCF) traits. Data were analyzed through a Bayesian bivariate animal model by using a reparameterization of Dickerson's model. The results obtained showed an important genetic determinism for all traits analyzed with heritability ranging from 0.09 to 0.67. The common environment litter effect also had an important effect on IMF (0.34) and its fatty acid composition (0.06-0.53) at slaughter. The additive genetic correlation between BFT and IMF (additive genetic correlation [r(g)] = 0.31) suggested that it would be possible to improve lean growth independent of the IMF with an appropriate selection index. Furthermore, the high additive genetic correlation (rg = 0.68) found between MUFA tissues would seem to indicate that either the LT or SCF could be used as the reference tissue for MUFA selection. The relevance of the crossbreeding parameters varied according to the traits analyzed. Backfat thickness at the fourth rib and the fatty acid profile of the IMF showed relevant differences between crosses, mostly due to line additive genetic effects associated with the Retinto line. On the contrary, those for IMF crosses were probably mainly attributable to heterosis effects. Particularly, heterosis effects were relevant for the Retinto and Entrepelado crosses (approximately 16% of the trait), which could be valuable for a crossbreeding system involving these lines.