The stability of two-layer stratified flow is analyzed utilizing as a stability criterion the condition that the celerity of kinematic internal waves dominated by friction and/or exchange of mass, be less than the celerity of intertia-dominated internal waves. This criterion for stability on scales large with respect to the depth is related to the well-known Vedernikov criterion for open-channel flow. The influence of bottom and interface friction on stability is examined for underflow. overflow, exchange flow and the case of coflowing layers. Taking into account non-uniformity of the velocity profiles is shown to increase the stability. Non-uniformity of the density profiles produces the opposite effect. The influence of small-scale mixing (entrainment) on the stability of underflow is also analyzed.