We present diffuse interface approximations for a step flow model in epitaxial growth. In this model, the motion of step edges of discrete atomic layers is determined by the time evolution of an introduced phase-field variable. In order to incorporate the attachment-detachment kinetics at step edges into the phase-field model a degenerate mobility-function is established. The model is used to simulate the evolution of a step train. (C) 2003 Elsevier B.V. All rights reserved.