Two transformation groups (t.g.) are called weakly disjoint if their product is ergodic. We characterize this relation for a certain class of t.g. and then prove that for (X, T) and (Y, T) in a certain family of t.g. (X, T) and (Y, T) are disjoint iff they have no nontrivial common factor. Finally, we generalize some disjointness relations of [2] and [4].