Social sciences are facing major and numerous methodological problems. So that these problems may be examined and solutions found. Take forexample the gap between empirical and theoretical research, the explanatory power of models, the relevance of multilevel models, the weakness ofcumulative knowledge, etc. These problems are well known, but seldom treated in depth.The Methodos Series, established by Robert Franck in 2002, and now edited in cooperation with me from 2003, is entirely concerned with these methods. I also participated to other methodological volumes, which I will consider later.Ten volumes are already published in the Methodos Series. You will find a detailed presentation of these volumes in the Springer website•I edited the second volume on Methodology and epistemology of multilevel analysis. Approaches from different social sciences (2003) which considers the view of different social science researchers (educational science, demography, epidemiology, statistics and economy) and of one philosopher, on this theme. •I am also the author of the tenth volume on: Probability and social science. Methodological relationships between the two approaches (2012) , which considers a dual approach and shed new lights on the history of probability, statistics and social sciences. It permits to solve a number of problems encountered during more than three centuries. The other authors or editors of Methodos volumes have examined and solved different methodological problems, arising in a great number of social sciences.•In a volume in French about cumulativity (La cumulativité en sciences sociales(2009) , edited by Bernard Walliser) I wrote a chapter on Demographic paradigms and cumulativity, where I examine how the plurality of demographic paradigms may however permit a non linear cumulativity.