The main aim of this article is to analyse the change of adult skills, as captured by cognitive skills assessed in PIAAC, across age cohorts, taking into account that the quality of schooling may change from one cohort to another. We estimate a model that relates numeracy and literacy skills to age, schooling, gender and variables related to both family background and labour market performance. The specification allows us to control for changes in the efficiency of the transformation of schooling into skills when drawing age-skill profiles. Our results show that the effect of ageing on skills, once isolated from cohort effects related to schooling, decreases monotonically across consecutive cohorts. The change of the efficiency of the transformation of schooling into both numeracy and literacy skills shows a remarkably similar pattern. Nonetheless, this change differs substantially between education levels, with the efficiency of the transformation of schooling into skills showing a steadier profile for intermediate than for higher education. Finally, empirical evidence is provided for the decomposition of the differences in the skill levels of the older vs. the prime age generations. The results suggest that the progressive expansion of schooling across younger generations partially offsets the negative effect of the irrepressible ageing of society on skills.