The study aims to describe the development of core-periphery differences in infant mortality trends in Finland from 1950 to 1984. The infant mortality trends in core and in periphery are described at three levels of spatial hierarchy: (1) nation, (2) province and (3) local hospital region. The main findings are: (1) at the national level: (a) the differences between core and periphery in infant mortality trends disappear by the mid 1960s, mainly due to the equalization of postneonatal mortality and (b) the diminishing of postneonatal mortality stops and the diminishing of especially the first-day mortality begins about the middle of 1960s, both in core and periphery; (2) in the province of Uundenmaan lääni there are no differences in infant mortality trends between the metropolitan area of Helsinki (core) and the rest of this province (periphery); (3) in the two local hospital regions the diminishing of infant mortality is significantly slower in periphery than in core. At present there is scarely any core-periphery variation in the trends of different components of infant mortality. This is a very remarkable fact when the achievements of the health and social policy of Finland are assessed. Several possible methodological, socio-economic, demographic and health care factors that may explain the differences in infant mortality trends between core and periphery at different levels of spatial hierarchy are discussed.