Genetic parameters pertaining to the same chemical characteristics of three porcine tissues, that is backfat (BF), perirenal fat (PF) and longissimus muscle (LM), were estimated in centrally tested Large White and Landrace pigs. Animals were fed ad libitum. They were slaughtered at an average BW of 99.6 kg, and samples of BF (both inner and outer layers) and LM were removed at the 13th to 14th rib level of the carcass on the day after slaughter. The data set included 2483 animals recorded for average daily gain (ADG; 35 to 100 kg), estimated carcass lean percentage (LEAN) and lean tissue growth rate (LTGR). Among these animals, around 950 pigs were recorded for lipid content (L%) and water content (W%) of BF and LM and for fatty acid composition (FAC) of BF, whereas FAC of LM was measured on 297 pigs and L%, W%, and FAC of PF on around 210 pigs. Heritabilities (h2) and genetic correlations (ra) were estimated using REML-animal model methodology. Estimates of h2 for L%, W% and FAC of BF, PF and LM were of moderate-to-high magnitude: for example 0.47 ± 0.09 for L% of LM, 0.59 ± 0.11 for W% of BF, 0.45 ± 0.08 for the ratio of polyunsaturated to saturated fatty acids (P/S) of BF, 0.61 ± 0.15 and 0.29 ± 0.10 for the coefficient of unsaturation of lipids (UNSAT, average number of double bonds of unsaturated fatty acids) of PF and LM, respectively. Genetic correlations of L% with P/S or UNSAT were strongly negative (from −0.4 to −0.9) in BF and LM, but not in PF. The ‘between-tissue’ genetic correlations for homologous compositional traits were far from being unity (e.g. ra = 0.57 ± 0.05 ‘between’ BF and PF for UNSAT). Genetic relationships between ADG and tissue compositional traits were globally weak. By contrast, genetic correlations were moderate-to-high between carcass leanness and tissue compositional traits, especially those of fat depots: for example −0.66 ± 0.14 between LEAN and L% of BF, 0.50 ± 0.07 between LEAN and UNSAT of PF, −0.44 ± 0.08 between LEAN and L% of LM, and 0.27 ± 0.03 between LEAN and UNSAT of LM. On the basis of the parameter estimates found here, breeding for higher LTGR is expected to increase the ratio of water to lipids and the unsaturation degree of lipids in subcutaneous BF and, to a lesser extent, in PF. Tissue composition and FAC of LM would be less affected.