On the base of nonlinear liquidus and solidus, an extended model for dendrite growth in bulk undercooled melts was developed under local non-equilibrium conditions both at the interface and in the bulk liquid. In terms of thermodynamic calculations of the phase diagram, the model predictions are relatively realistic physically, since few fitting parameters are used in the model predictions. Adopting three characteristic velocities, i.e. the critical velocity of absolute solute stability (VC*), the velocity of maximal tip radius (VRm), and the velocity of bulk liquid diffusion (VD), a quantitative agreement is obtained between the model predictions and the experimental results in undercooled Ni-0.7%B and Ni-1%Zr (molar fraction) alloys, and the overall solidification process can be categorized.