The paper considers the modern discussion about Roman demography of the Republic presented in works of modern foreign scholars. The author discusses the most important reconstructions made by E. Lo Cascio, L. de Ligt, S. Hin and others. Не points out the historical problems which must be solved for a better understanding of demographic development of Rome in this period. The criteria and functions of the Roman census, the factors which impacted on Roman census figures of the Republic are meant