This paper uses the first available vital statistics by citizenship for Greece to estimate current fertility among immigrants and natives. Subsequently, population projections are employed to assess the demographic effects of migrant/native fertility and of immigration on the country's population for the period 2005-2025. It is estimated (2005) that immigrants exhibit earlier childbearing and higher total fertility (2.12) than natives (1.24). Of the ethnic groups considered, Albanians have the highest and Bulgarians the lowest rates. Although births to immigrants represent a considerable share (16.5%) their impact on overall fertility is very limited. The projections reveal that the ageing of the country's population is inevitable as the effects of variant levels of foreign/native fertility are minor and immigration, in spite of being the most important component having a favorable impact, cannot offset this process. The concept of Replacement Migration is an infeasible solution as it would require an unattainable intake of 4 million newcomers.