A possibility for a feedback control of morphological instability of the interface of a binary crystal growing from its melt in directional solidification process is theoretically investigated. As a feedback control method external melt heating in the vicinity of the melt/crystal interface is considered, with the heating parameters depending, through the control loop, on the morphology of the solidification front perturbations. Linear stability analysis of the corresponding mathematical problem is performed taking into account Solute diffusion in the melt, thermal diffusion in crystal and melt, latent heat, as well as the effects of the constitutional undercooling and the melt/crystal interfacial tension. Neutral stability curves are plotted and it is shown that the chosen feedback control can substantially increase the threshold value of the morphological number above which the morphological instability occurs. Dependence of the feedback control effect on the parameters characterizing the external melt heating. as well as on the physico-chemical parameters of the system, is analyzed. (C) 2002 Elsevier Science B.V. All rights reserved.