The effect of deviations from equilibrium at the solid-liquid interface during steady-state directional solidification of binary alloys has been analysed. The analysis includes the solute trapping region wherein freezing is accompanied by an increase in the chemical potential of the solute as well as the domain in which solidification is associated with a decrease in chemical potential of both the components. The limits to constitutional undercooling and the interface liquid compositions at various interface velocities in the solute trapping region have been derived using a thermodynamic approach.