  The method of solving the Bethe-Salpeter equation in Minkowski space,
developed previously for spinless particles, is extended to a system of two
fermions. The method is based on the Nakanishi integral representation of the
amplitude and on projecting the equation on the light-front plane. The
singularities in the projected two-fermion kernel are regularized without
modifying the original BS amplitudes. The numerical solutions for the J=0 bound
state with the scalar, pseudoscalar and massless vector exchange kernels are
found. Binding energies are in close agreement with the Euclidean results.
Corresponding amplitudes in Minkowski space are obtained.
