Background: We investigated associations between behaviour problems and verbal and nonverbal cognitive abilities at 2, 3 and 4 years of age both for the entire distribution and for the lowest 5% and 10% of the verbal and nonverbal cognitive disabilities. Methods: A community sample of 4,000 pairs of twins born in England and Wales in 1994 and 1995 was assessed by their parents at 2, 3 and 4 years using the Revised Rutter Parent Scale for Preschool Children (RRPSPC, behaviour problems), the MacArthur Communicative Development Inventory (MCDI, verbal development), and the Parent Report of Children's Abilities (PARCA, nonverbal cognitive development). Results: For the entire sample, behaviour problem scores were modestly associated with lower MCDI and PARCA scores – correlations were less than .30. Similarly modest effect sizes were found for relationships between behaviour problem scores and the lowest 5% and 10% of the MCDI and of the PARCA distributions. Associations were stronger for nonverbal than for verbal development, increased from 2 to 3 to 4 years, and, at the extremes of the distributions, were stronger for boys than for girls. Multivariate genetic analyses indicated that both genetic and shared environmental factors mediate the links between behaviour problems and cognitive development both for the total distribution and for the extremes. Genetic links may be stronger for the extremes than for the total sample. Conclusions: We conclude that, in this community sample of young children, associations between behaviour problems and verbal and nonverbal cognitive development are generally modest for the entire distribution and are no greater at the extremes than expected on the basis of the associations for the entire distribution.