Further analysis of the M-S interface stability theory predicts a new phenomenon, the high gradient absolute stability (HGAS); that is, when temperature gradient exceeds a critical value, the solidification interface becomes absolutely stable no matter how large solidification velocity is. The critical temperature gradient for HGAS is explicitly evaluated by incorporating mathematical deduction with numerical calculation. The critical conditions for HGAS of several typical alloys are modified by inserting a velocity-dependent partition coefficient and a velocity-dependent slope of the "kinetic liquidus" into the HGAS analysis. These nonequilibrium interface kinetic effects decrease the predicted critical temperature gradient for HGAS.