Principal components and canonical correla- tions are at the root of many exploratory data mining techniques and provide stan- dard pre-processing tools in machine learn- ing. Lately, probabilistic reformulations of these methods have been proposed (Roweis, 1998; Tipping & Bishop, 1999b; Bach & Jor- dan, 2005). They are based on a Gaussian density model and are therefore, like their non-probabilistic counterpart, very sensitive to atypical observations. In this paper, we in- troduce robust probabilistic principal compo- nent analysis and robust probabilistic canon- ical correlation analysis. Both are based on a Student-t density model. The resulting prob- abilistic reformulations are more suitable in practice as they handle outliers in a natural way. We compute maximum likelihood esti- mates of the parameters by means of the EM algorithm.