Most research on trends in socioeconomic fertility differences focus on cohort total fertility. This study asks how cohort trends in parity-specific fertility differ across educational segments for men and women, and what role multi-partner fertility plays in these trends. The study used Finnish and Swedish register data on cohorts born in 1940–1973/1978. The main analyses use parity progression ratios. Ordinary ratios were contrasted with ratios on births to first reproductive partner. Among

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... w- and medium-educated persons we observe parity polarization, where both childlessness and higher parity (3+) births increase, largely reflecting increases in multi-partner fertility. Highly educated men and women more often have exactly two children. We demonstrate that cohort total fertility can mask significant parity-specific trends across educational groups, and that changes in multi-partner fertility can be a part and parcel of cohort trends in socioeconomic fertility differentials.