In this paper, we shall be concerned with the question of what conditions on minimal transformation groups will guarantee that they are disjoint. Generalizing a result of I. Bronstein about lifting of minimality through group extensions to associated bitransformation groups, we prove that in a large class of transformation groups, disjointness is equivalent to disjointness of their maximal equicontinuous factors. In the abelian case, this means that disjointness is equivalent to no common factor in the class of flows discussed.