This paper theoretically investigates the possibility for feedback control of morphological instability of the melt/crystal interface during the directional growth of a binary crystal from its melt. The control method involves applying external heating within the melt in the vicinity of the melt crystal interface, with the heating parameters depending, through the control loop. on the morphology of the solidification front. Linear stability analysis of the corresponding mathematical problem is performed, accounting the solute diffusion in the melt, the thermal diffusion in crystal and melt, the latent heat release, as well as the effects of the constitutional undercooling and melt; crystal interfacial tension. Neutral stability curves are plotted and it is shown that the chosen feedback control approach can substantially increase the threshold for onset of morphological instability. The dependence of feedback control improvement on parameters characterizing the external melt heating as well as on the physico-chemical parameters of the system, is investigated. Finally, the feedback-induced oscillatory instabilities are analyzed, and it is shown that they can be suppressed by an appropriate choice of the control parameters. (C) 2002 Elsevier Science B.V. All rights reserved.