The aim of this work was to study the, so far, unexplored possibility that non-genetic inheritance of animal behavioral characteristics could depend on the state of the parents at the time of conception, by studying inheritance of high and low motor and exploratory activity in the first generation of rats. In this study, we measured the levels of motor and exploratory activity in rats at the ages of 2 and 5 months. Male and female rats were mated at the age of 5 months. The following groups were used: male and female rats with high motor activity at ages of 2 and 5 months (ACT+); male and female rats with high activity at the age of 2 months, but low activity at the age of 5 months (ACT–); male and female rats with low activity at the ages of 2 and 5 months (PAS–); male and female rats with low activity at the age of 2 months, but high activity at the age of 5 months (PAS+). Significant differences in the severity of exploratory activity were found between the offspring of ACT+ and ACT– rats. Moreover, these differences were observed only in males, and not in females. Differences between the offspring of PAS+ and PAS– rats were observed in both the male and female rats. The motor activity of animals in the period from 20 minutes after the start of registration did not differ between groups. Thus, it can be considered that individual characteristics of general motor activity are due to genetically inherited factors, while differences in the level of exploratory activity, apparently, are formed due to non-genetic influences from parents during mating.