By allowing the segregation coefficient and interface temperature to depend on interface speed in a thermodynamically-consistent way, the non-equilibrium effects are incorporated into a linear stability analysis of planar front. The absolute stability limit of the cellular mode is modified. A new oscillatory instability is found, which leads to the formation of solute bands in the solid, and its absolute-stability limit is determined by solute trapping and kinetics. The results of this theory are in agreement with observations.