Research about the Flynn effect, the secular rise in IQ, is heavily based on conscript data from successive male birth cohorts. This inevitably means that two distinct phenomena are mixed: fertility differences by IQ group (‘compositional Flynn effect’), and any difference between parents and children (‘within-family Flynn effect’). Both will influence trends in cognitive ability. We focused on the latter phenomenon, exploring changes in cognitive abilities during adolescence within one generation, and between two successive generations within the same family. We identified determinants and outcomes in three linked generations in the Stockholm Multigenerational Study. School and conscript data covered logical/numerical and verbal scores for mothers at age 13, fathers at 13 and 18, and their sons at 18. Raw scores, and change in raw scores, were used as outcomes in linear regressions. Both parents’ abilities at 13 were equally important for sons’ abilities at 18. Boys from disadvantaged backgrounds caught up with other boys during adolescence. Comparing fathers with sons, there appeared to be a positive Flynn effect in logical/numeric and verbal abilities. This was larger if the father had a working-class background or many siblings. A Flynn effect was only visible in families where the father had low general cognitive ability at 18. We conclude that there is a general improvement in logical/numeric and verbal skills from one generation to the next, primarily based on improvement in disadvantaged families. The Flynn effect in Sweden during the later 20th century appears to represent a narrowing between social categories.