We study a system combining adaptive feedback cancellation and adaptive filtering connecting inputs from both ears for signal enhancement in hearing aids. For the first time, such a binaural system is analyzed in terms of system stability, convergence of the algorithms, and possible interaction effects. As major outcomes of this study, a new stability condition adapted to the considered binaural scenario is presented, some already existing and commonly used feedback cancellation performance measures for the unilateral case are adapted to the binaural case, and possible interaction effects between the algorithms are identified. For illustration purposes, a blind source separation algorithm has been chosen as an example for adaptive binaural spatial filtering. Experimental results for binaural hearing aids confirm the theoretical findings and the validity of the new measures.