The power of the Kolmogorov–Smirnov (KS) test for the occurrence of signals in signal detection problems with Gaussian white noise is investigated. Employing the approach of Milbrodt and Strasser (1990) a principal components decomposition of the curvature of the power function at the hypothesis is established and computed. This decomposition indicates that the test has reasonable power only for a small number of orthogonal directions, and shows how the test distributes its power over all alternatives. Comparisons with the powers of some alternative procedures are made.