We study dynamical mass generation for fermions in the Yukawa and the supersymmetric Wess-Zumino (WZ) models. It is found that above a critical coupling fermion mass can be generated dynamically in the Yukawa model, whereas in the WZ model the fermion does not acquire mass. We also show that the supersymmetry (SUSY) preserving solution is permitted and hence the scalars may not acquire mass either. ©1999 American Institute of Physics.