The stability of discrete time kinematic sensor-based control of robots is investigated in this paper. A hierarchical inner-loop/outer-loop control architecture common for a generic robotic system is considered. The inner loop is composed of a servo-level joint controller and higher level kinematic feedback is performed in the outer loop. Stability results derived in this paper are of interest in several applications including visual servoing problems, redundancy control, and coordination/synchronization problems. The stability of the overall system is investigated taking into account input/output delays and the inner loop dynamics. A necessary and sufficient condition that the gain of the outer feedback loop has to satisfy to ensure local stability is derived. Experiments on a Kuka K-R16 manipulator have been performed in order to validate the theoretical findings on a real robotic system and show their practical relevance.