The aim of this paper is to test for stochastic monotonicity in intergenerational socio-economic mobility tables. In other words we question whether having a parent from a high socio-economic status is never worse than having one with a lower status. We ?rst test a set of 149 intergenerational mobility tables in 35 different countries and ?nd that monotonicity cannot be rejected in hardly any table. We then explain how a number of covariates such as education, cognitive and non-cognitive skills can be used to investigate whether monotonicity still holds after conditioning on these variables. Based on the NCDS cohort data from the UK, our results provide evidence that monotonicity holds even conditionally.