Abstract This paper observes change since 1970s in proportion of men and women having only one child during their reproductive life, and examines their sociodemographic characteristics. The aim is to explore significant variables of complement of parity progression ratio to second birth (1-A1). First, we present theories, findings, and results relating to single-child family model in Europe. Then, we perform a multivariate analysis, with dependent variable of model being fact of not having had a second child ten years after birth of a first child in stable unions. 1. Introduction When men and women are asked about their ideal family size or number of children they would like to have, answer is seldom one child. There are many prejudices, based on work of psychologists, child psychiatrists, and other specialists, concerning difficulties parents are supposed to have in successfully bringing up a child who is deprived of a brother or sister.3 And yet having only one child is much more frequent than generally supposed. In France, for example, this is case for one woman in five, a proportion that has not greatly changed over time. The false impression of rarity is due to a statistical fact: since, by definition, number of children from large families is large, we more frequently come across people from families of three children or more than those who are only children, and latter have almost never represented more than 10% of a cohort (Toulemon 2001). Why then, despite these prejudices, do so many couples only have one child? Although in some cases reason may be the of life (late union, separation, difficulties in conceiving, etc.), comparison with United Kingdom, where most probably same vagaries occur but where frequency of one-child families is barely half that of France, shows that gap between stated desire or ideal and observed reality is due, at least in part, to deliberate behavior. In this article we attempt to determine who are women and men who have only one child, by identifying most significant criteria: What is role of biological or physiological factors related to late childbearing? What is role of specific union histories with early union dissolution not followed by repartnering? To what extent can these men and women be said to have made a choice? Does this happen more frequently in particular socio-occupational categories? What is role of cultural factors and influence of family history, such as own sibship size? These questions about socio-cultural factors that appear to favor one-child families in France are of particular relevance at a time when this family pattern is spreading across a number of Central European countries and in Southern Europe, notably Italy and Spain. The frequency of one-child families is one reason for current low level of fertility in these countries, along with a high proportion of childlessness. Although research into factors associated with childlessness is abundant and relatively long-established, only recently has demographic literature featured articles devoted specifically to characteristics of one-child families and factors associated with birth of a second child (see, for example, Jefferies 2001; Olah 2003; Kreyenfeld and Zabel 2005; Torr and Short 2004; Prskawetz and Zagaglia 2005; Gerster et al. 2007; Parr 2007). This recent surge in interest is clearly due to rapid increase in proportion of one-child families in certain countries. In first part of article, we present an overview of comparative frequency of childless women and one-child mothers in Europe, using statistical data we have collected. We then review various hypotheses that may explain why women and men restrict their number of children to one. Part three describes our data and methodology. …