The initial stages of contact melting and eutectic crystallization in sharp concentration gradients between two crystalline components are studied and simulated analytically and numerically. Contact melting is shown to become possible only after the formation of some critical width of solid solutions. Crystallization in the sharp concentration gradient may lead to the formation of periodic structures in the interface vicinity. In addition, at least for the eutectic systems of Ag–Cu type, the threshold temperature should exist, under which the “precipitation + growth” mechanism of crystallization may be changed to “polymorphic crystallization with eutectic composition + subsequent spinodal decomposition.”