In recent experiments on the growth of localized disturbances in a Blasius boundary layer, Medeiros & Gaster (1999a, b) observed that the development of nonlinear effects depends markedly on the initial phase of their imposed disturbance. Here, a simple explanation of this phenomenon is proposed. Because the disturbance is localized in space and time, it has a spread of wavenumbers and frequencies: among these are components which can initiate a pair of resonant subharmonic waves with well-determined phase, which are then amplified by the familiar three-wave resonance mechanism. The amplitude attained after some time is strongly phase-dependent, consistent with the experimental observations.