We study the morphological instabilities of a dilute binary alloy during directional solidification into a time-periodic, oscillatory molten zone by modulating the solute field. The basic state, in which the flat melt-solid interface advances in a sinusoidal way, is solved analytically by expanding the governing equations in terms of the assumed-small amplitude of modulation. A linear stability analysis is then performed on the interface considering two specific instability modes: synchronous and subharmonic modes. We find the original Mullins-Sekerka instability can be stabilized synchronously by the imposed modulation. The subharmonic mode occurs with smaller wave numbers and is less critical than the synchronous Mullins-Sekerka mode. (c) 2004 Elsevier B.V. All rights reserved.