In this paper we introduce the generalized fluctuation test for monitoring structural changes and establish a result characterizing the limiting behavior of this class of tests. As applications of the generalized fluctuation test, tests based on the maximum and range of the fluctuation of moving estimates are proposed. We also derive the boundary functions for the proposed tests and tabulate simulated critical values. Our simulations indicate that these tests compare favorably with the recursive-estimates-based test considered by Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) when a change occurs late.