On the basis of an extended Flory-Huggins expression for the mixing free energy of the long-chain binary polymer blend, we showed that liquid-liquid demixing can be driven solely by the propensities of crystallization differing with respect to components. Demixing prior to crystallization on cooling was demonstrated by dynamic Monte Carlo simulations of the lattice model for a symmetric polymer blend where only one component is crystallizable. We discussed the implications of this principle to several experimental observations including the (in) compatibility of polymer chains with different stereochemical compositions, the memory effect of polymer crystallization, and the spinodal decomposition at an early stage of polymer crystallization. (C) 2003 American Institute of Physics.