Summary: This paper addresses a number of open problems concerning the generalized likelihood ratio (GLR) rules for online detection of faults and parameter changes in control systems. It is shown that with an appropriate choice of the threshold and window size, these GLR rules are asymptotically optimal. The rules are also extended to nonlikelihood statistics that are widely using in monitoring adaptive algorithms for system identification and control by establishing Gaussian approximations to these statistics when the window size is chosen suitably. Recursive algorithms are developed for practical implementation of the procedure, and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate.