This study examines cognitive and non-cognitive skills and their transmission from parents to children as one potential candidate to explain the intergenerational link of socio-economic status. Using representative data from the German Socio-Economic Panel Study, we contrast the impact of parental cognitive abilities (fluid intelligence, crystallized intelligence) and personality traits (Big Five, locus of control) on their adolescent and young adult children's traits with the effects of parental background and childhood environment. While for both age groups intelligence and personal traits were found to be transmitted from parents to their children, there are large discrepancies with respect to the age group and the type of skill. The intergenerational transmission effect was found to be relatively small for adolescent children, with correlations between 0.12 and 0.24, whereas the parent-child correlation in the sample of adult children was between 0.19 and 0.27 for non-cognitive skills, and up to 0.56 for cognitive skills. Thus, the skill gradient increases with the age of the child. Furthermore, the skill transmission effects are virtually unchanged by controlling for childhood environment or parental education, suggesting that the socio-economic status of the family does not play a mediating role in the intergenerational transmission of intelligence and personality traits. The finding that non-cognitive skills are not as strongly transmitted as cognitive skills, suggests that there is more room for external (non-parental) influences in the formation of personal traits. Hence, it is more promising for policy makers to focus on shaping children's non-cognitive skills to promote intergenerational mobility. Intergenerational correlations of cognitive skills in Germany are roughly the same or slightly stronger than those found by previous studies for other countries with different institutional settings. Intergenerational correlations of non-cognitive skills revealed for Germany seem to be considerably higher than the ones found for the U.S. Hence, skill transmission does not seem to be able to explain cross-country differences in socio-economic mobility.