Image processing systems that contain feedback loops sometimes become unstable: they oscillate in space and time, which is fascinating but undesirable. These oscillations can be avoided if the system satisfies certain stability conditions. For purely time-dependent (one-dimensional) linear systems some stability tests are known, for example, from electronics. In this paper we consider multidimensional (space/time) systems. The resulting stability theorems are applied to some examples, such as iterative image processing, analog computing, etc. Finally, some considerations for the treatment of nonlinear systems are given.