Although certain iterative optical processors promise algorithmic convergence at the speed of light, little attention is normally given to the consequences of different path lengths required within the processor on the processor performance. The resulting clock skew can have significant degrading effects on the predicted accuracy, stability, and speed of the processor. A similar problem occurs in iterative asynchronous artificial neural networks when, for example, the time delay between two neurons is proportional to their physical separation. In this paper, we show that in the absence of temporal dispersion, certain iterative algorithms have stable steady-state solutions that are independent of clock skew. Examples include stable linear feedback and feedback using soft (slowly varying) nonlinearities. Both are special cases of using a contractive operation in the feedback path. Such processing algorithms can have stable steady-state solutions that are independent of clock skew. Feedback using hard nonlinearities, on the other hand, can result in either an oscillatory or a steady-state solution that depends on the clock skew.