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Non‐genetic information (epigenetic, microbiota, behaviour) that results in different phenotypes in animals can be transmitted from one generation to the next and thus is potentially involved in the inheritance of traits. However, in livestock species, animals are selected based on genetic inheritance only. The objective of the present study was to determine whether non‐genetic inherited effects play a role in the inheritance of residual feed intake (RFI) in two species: pigs and rabbits. If so, the path coefficients of the information transmitted from sire and dam to offspring would differ from the expected transmission factor of 0.5 that occurs if inherited information is of genetic origin only. Two pigs (pig1, pig2) and two rabbits (rabbit1, rabbit2) datasets were used in this study (1,603, 3,901, 5,213 and 4,584 records, respectively). The test of the path coefficients to 0.5 was performed for each dataset using likelihood ratio tests (null model: transmissibility model with both path coefficients equal to 0.5, full model: unconstrained transmissibility model). The path coefficients differed significantly from 0.5 for one of the pig datasets (pig2). Although not significant, we observed, as a general trend, that sire path coefficients of transmission were lower than dam path coefficients in three of the datasets (0.46 vs 0.53 for pig1, 0.39 vs 0.44 for pig2 and 0.38 vs 0.50 for rabbit1). These results suggest that phenomena other than genetic sources of inheritance explain the phenotypic resemblance between relatives for RFI, with a higher transmission from the dam's side than from the sire's side.