The article draws on the concept of 'replacement migration', widely presented by the Population Division of the UN Department of Economic and Social Affairs in 2000 and 2001, which elaborated a concept and conducted a comprehensive analysis of international migration as a solution to the problem of population declines and demographic ageing. This concept was applied as an example to selected countries in the world, the European region, and the European Union as a whole. It involves calculating the number of foreign migrants necessary to completely offset future changes in the size or age structure of the given country's population as a result of the predicted demographic trends. The following article describes the formulation of this concept and looks at its application on a general methodological level and in the specific case of the Czech Republic. A detailed description is given not just of the model used but also of its internal and external assumptions. The constructed model is then applied towards determining the necessary number of 'replacement migrants' in order to prevent a significant change in the Czech Republic in: 1) the total size of the population, 2) the average age of the population, 3) the percentage of people of working age, and 4) the ratio of people of post-productive to productive age. With the aid of the results the authors clearly demonstrate that while international migrants could effectively help maintain the current size of the population, they would not be able to prevent the continued ageing of the population or even have a decisive impact on the course of this process. With these findings the authors hope to contribute to the debate on the topic of the ageing population in the Czech Republic, and they call strongly for more intensive and especially more effective preparations for this real and unavoidable era in the development of Czech society.