The presented analysis of mass transfer in the systems "anisotropic crystal-inclusion of solution in melt" has revealed the novel non-stationary nonlinear effects referring to motion of the solid-liquid interfaces and migration of the entire inclusion. In particular, it has been found that the velocity of the inclusion migration due to temperature gradient exhibits unusually high sensitivity to small oscillations of the average temperature of the system. At relatively small deviations of the average temperature of the whole system, the dependence of the migration velocity on the inclusion size qualitatively differs from the case of strictly stationary thermal conditions. Further it is shown that migration of the liquid flat interlayer becomes possible even in the absence of temperature gradient when the symmetry of properties of the interfaces and/or the symmetry of temperature oscillations are distorted. It is demonstrated that the shape of the liquid inclusion can be controlled by altering the amplitude and profile of temperature oscillations. The obtained results are essential for understanding any experiments associated with the processes of dissolution-crystallization involving small volumes of solutions in melts. (C) 2009 Elsevier B.V. All rights reserved.