A socioeconomically differentiated population evolves through differential fertility, mortality, marriage, and migration of socioeconomic groups, as well as through intergenerational social mobility. If mobility processes are non-Markovian -- that is, include net associations of socioeconomic status across more than two generations -- then the demography of mobility is more complex. Many types of multigenerational effects are possible, including those that work through mobility itself and those that work through demographic processes. In some circumstances, multigenerational effects may also arise from remote ancestral conditions, as well as from intergenerational connections between the characteristics of specific more proximate kin. The short and longer run implications of these effects also depend on whether mobility processes depend on the characteristics of one sex or both sexes. This paper describes this array of possible multigenerational effects, shows the conditions under which the socioeconomic characteristics of an individual in one generation may affect future generations, and illustrates these results with data from the Qing Dynasty era of China and the contemporary United States.