When a two-component melt is solidifying from a bottom boundary, convection may be induced in an unstable compositional boundary layer. In this study, the onset of compositional convection during time-dependent solidification is investigated by using similarly transformed disturbance equations. The critical Darcy-Rayleigh numbers based on the mushy-layer thickness are found numerically for various Lewis numbers, superheats, and Darcy numbers. In aqueous ammonium chloride solution, the critical conditions at the onset of mushy-layer-mode convection are consistent with existing theoretical and experimental results. For small superheats and Darcy numbers, the present predictions for boundary-layer-mode instabilities approach the results of convective instability during steady solidification. (C) 2004 Elsevier B.V. All rights reserved.