Advancing paternal and maternal age have both been associated with risk for autism spectrum disorders (ASD). However, the shape of the association remains unclear, and results on the joint associations is lacking. This study tests if advancing paternal and maternal ages are independently associated with ASD risk and estimates the functional form of the associations. In a population-based cohort study from five countries (Denmark, Israel, Norway, Sweden and Western Australia) comprising 5 766 794 children born 1985-2004 and followed up to the end of 2004-2009, the relative risk (RR) of ASD was estimated by using logistic regression and splines. Our analyses included 30 902 cases of ASD. Advancing paternal and maternal age were each associated with increased RR of ASD after adjusting for confounding and the other parent's age (mothers 40-49 years vs 20-29 years, RR=1.15 (95% confidence interval (CI): 1.06-1.24), P-value<0.001; fathers⩾50 years vs 20-29 years, RR=1.66 (95% CI: 1.49-1.85), P-value<0.001). Younger maternal age was also associated with increased risk for ASD (mothers <20 years vs 20-29 years, RR=1.18 (95% CI: 1.08-1.29), P-value<0.001). There was a joint effect of maternal and paternal age with increasing risk of ASD for couples with increasing differences in parental ages. We did not find any support for a modifying effect by the sex of the offspring. In conclusion, as shown in multiple geographic regions, increases in ASD was not only limited to advancing paternal or maternal age alone but also to differences parental age including younger or older similarly aged parents as well as disparately aged parents.