This article presents (a) mathematical models for analyzing patterns of mobility and (b) statistical methods for testing whether observed patterns are congruent with patterns predicted by the models. To illustrate the application of these rather general models and methods, we reanalyze data on intergeneration social mobility in Britain and in Denmark which were studied earlier by Glass and his co-workers, by Svalastoga, and by White. We find, for example, that White's main results require modification. His predictions differ from the observed data in statistically significant ways, whereas the models introduced herein lead to predictions that fit the data well. Using the models and methods developed in the present article, we shall propose and test the theory that "status inheritance" from father to son is operative within certain limits:​ on the one hand there is "status inheritance" in every social stratum;​ but on the other hand for an individual who actually moves out of his father's stratum-either up or down-his own social status is, in a certain sense, independent of his father's status. When this theory is properly qualified, we find that it is supported by the British and Danish data.