Sweden has, as a whole nation, the oldest continuous population register of births, including twin and higher multiple maternities, starting in the 17th century. Until the 1920s, the rates of multiple maternities in Sweden were among the highest known among Europeans. Strong secular and regional fluctuations were noted. Some of the eastern counties showed especially marked decreasing trends. The twinning rate had no clear associations with the anthropometric and serological data. In this paper we study the temporal and regional variations of the twinning rate in the 25 counties of Sweden from 1751 to 1960. Different statistical methods were applied in order to test the hypothesis that, irrespective of the initial levels, the twinning rates for the counties converge towards a common low level. We present and interpret a geometrical model for the trends of the regional twinning rates. We also analyze the regional heterogeneity using the ranges and the coefficients of variation of the regional twinning rates. All the methods gave consistent results, supporting our convergence hypothesis that the regional differences in the twinning rate are gradually disappearing. In addition, this study supports our earlier findings that the regional heterogeneity cannot be explained by differences in the distribution of maternal age and parity. We suggest that the convergence may be caused by increased urbanization and industrialization and by the increased interregional migration of citizens as a consequence of better communications, which lead to the breaking up of isolates and decreased endogamy.