  The fixed point actions for Wilson and staggered lattice fermions are
determined by iterating renormalization group transformations. In both cases a
line of fixed points is found. Some points have very local fixed point actions.
They can be used to construct perfect lattice actions for asymptotically free
fermionic theories like QCD or the Gross-Neveu model. The local fixed point
actions for Wilson fermions break chiral symmetry, while in the staggered case
the remnant $U(1)_e \otimes U(1)_o$ symmetry is preserved. In addition, for
Wilson fermions a nonlocal fixed point is found that corresponds to free chiral
fermions. The vicinity of this fixed point is studied in the Gross-Neveu model
using perturbation theory.
