Abstract: Positive k-th intermediate Ricci curvature on a manifold of dimension n, to be denoted by Rick > 0, is a condition that interpolates between positive sectional and positive Ricci curvature (when k=1 and k=n-1 respectively). It follows from the definition that the smaller the k, the more restrictive the condition Rick > 0. In this talk we will discuss these curvatures conditions on homogeneous spaces with either their normal metrics or those induced by a homogeneous bundle.