Conduct problems in children and adolescents affect individuals, families, and their environment. The aetiology of conduct problems involves a combination of genetic and environmental risk factors, many of which are inherently linked to parental characteristics given parents’ central role in children’s lives across development. It is important to disentangle to what extent links between parental characteristics and children’s behaviour are due to transmission of genetic risk or due to environmentally mediated genetic influences on offspring behaviour (i.e., genetic nurture). We used 31,346 genotyped mother-father-child trios from the Norwegian Mother, Father and Child Cohort Study (MoBa), testing genetic transmission and genetic nurture effects on conduct problems using 12 polygenic scores (PGS) spanning psychiatric conditions, substance use, education-related factors, and other risk factors. Among genotyped trios, maternal reports of conduct problems at age 8 years were available for 15,516 children. We found significant genetic transmission effects on conduct problems for 11 out of 12 PGS (strongest positive association: PGS for smoking, β = 0.07 95% confidence interval = [0.05, 0.08]; strongest negative association: PGS for education, β = –0.04, 95% confidence interval = [¬–0.06, –0.02]). Conversely, we did not find strong evidence for genetic nurture effects for child conduct problems using our selection of PGS. Our findings provide evidence for genetic transmission in the association between parental characteristics like psychiatric conditions or risk behaviours and child conduct problems. Our results may also indicate that genetic nurture is of limited aetiological importance for conduct problems—though effects of small magnitude or effects via parental traits not captured by the included PGS remain a possibility.