STUDY QUESTION: The aim of the study was to analyse trends in the rate of natural conceptions (RNC) among birth cohorts of women born during the period 1960-1984. SUMMARY ANSWER: In this nationwide study of Danish-born female cohorts born during the period 1960-1984, we found a gradual decline in the RNC with successive birth cohorts. WHAT IS KNOWN ALREADY: Our results confirm the findings from a previous study on trends in RNC among native Danish women. STUDY DESIGN, SIZE, DURATION: This is a register-based cohort study. Our data set included 803 435 native Danish women born in 1960-1984, of whom 68.2% had conceived at least one child as of 1 January 2008, by which time the follow-up was terminated. PARTICIPANTS/MATERIALS, SETTING, METHODS: Data from Danish national registers were linked at the individual level using unique personal numbers assigned at birth to each resident. We analysed the data for the cohorts of native Danish women born in 1960-1984 and resident in Denmark in 2008. For these cohorts, we estimated the RNC per woman, defined as the mean number of live births minus live births after assisted reproductive technology (ART) plus the mean number of induced abortions. Births, abortions and births after ART were partly projected for the younger cohorts who had not finished their reproductive years before 2008. In addition, we looked at trends in hormonal contraception use. MAIN RESULTS: In the main projection scenario, the RNC gradually declined with successive cohorts from 2.39 among women born in 1960 to 2.15 among women born in 1984, with stable values of 2.15-2.16 projected in the youngest cohorts analysed, 1979-1984. The projected decline was a consequence of a decrease in induced abortion rates and an increase in the use of ART among the younger cohorts. Furthermore, we projected a cohort increase in the share of women without natural conceptions. LIMITATIONS, REASONS FOR CAUTION: A considerable portion of the results was based on projections, which involve uncertainty, especially concerning the results for women born in 1980 and later. In addition, information on IUI could not be included, which led to underestimation of the frequency of births after ART treatment. WIDER IMPLICATIONS OF THE FINDINGS: The results of our study contribute new insights to the research field of declining fertility rates in Europe and many other parts of the world.