The purpose of this study was to determine whether rats selectively bred for low and high response to aerobic exercise training co‐segregate for differences in muscle adaptations to ladder‐climbing resistance training. Five high‐responder (HRT) and five low‐responder (LRT) rats completed the resistance training, while six HRT and six LRT rats served as sedentary control animals. Before and after the 6 week intervention, body composition was determined by dual energy X‐ray absorptiometry. Before tissue harvesting, the right triceps surae muscles were loaded by electrical stimulation. Muscle fibre cross‐sectional areas, nuclei per cell, phosphorylation status of selected signalling proteins of mTOR and Smad pathways, and muscle protein, DNA and RNA concentrations were determined for the right gastrocnemius muscle. The daily protein synthesis rate was determined by the deuterium oxide method from the left quadriceps femoris muscle. Tissue weights of fore‐ and hindlimb muscles were measured. In response to resistance training, maximal carrying capacity was greater in HRT (∼3.3 times body mass) than LRT (∼2.5 times body mass), indicating greater improvements of strength in HRT. However, muscle hypertrophy that could be related to greater strength gains in HRT was not observed. Furthermore, noteworthy changes within the experimental groups or differences between groups were not observed in the present measures. The lack of hypertrophic muscular adaptations despite considerable increases in muscular strength suggest that adaptations to the present ladder‐climbing training in HRT and LRT rats were largely induced by neural adaptations.