A bounded input power-bounded output power stability criterion is derived for a class of single loop control systems having a memoryless, time-invariant, non-linear operator and a causal operator in the loop. The result is established by showing that a system from this class maps the Marcinkiewicz space ..,/'/2 into itself. When the causal operator is further restricted to be a time-invariant, linear operator characterized by a convolution with a suitably restricted kernal, the main ingredient of the criterion can be replaced by the Popov criterion. BENE~ [3] has pointed out that the existence of a system response in J[2 is of practical significance. The input to a system is often a "noise wave"--a sample function #(., o9) of a stochastic process, where toef~, a probability space-which is neither bounded nor square-integrable, that is, not of finite energy. If the process has finite power and is stationary, then, for almost all o~fl, the previously indicated limit exists and #(', to)e,,/(2. That being the case, it is quite reasonable to establish conditions under which #E.,~¢2 implies h~.,¢[2.*