  The chiral limit $~\kappa \simeq \kappa_c(\beta)~$ in lattice gauge theories
with Wilson fermions and problems related to near--to--zero ('exceptional')
eigenvalues of the fermionic matrix are studied. For this purpose we employ
compact lattice QED in the confinement phase. A new estimator $~\mpr_{\pi}~$
for the calculation of the pseudoscalar mass $~m_{\pi}~$ is proposed which does
not suffer from 'divergent' contributions at $\kappa \simeq \kappa_c(\beta)$.
We conclude that the main contribution to the pion mass comes from larger
modes, and 'exceptional' eigenvalues play {\it no} physical role. The behaviour
of the subtracted chiral condensate $~\langle \psb \psi \rangle_{subt}~$ near
$~\kappa_c(\beta)~$ is determined. We observe a comparatively large value of
$~\langle \psb \psi \rangle_{subt} \cdot Z_P^{-1}~$, which could be interpreted
as a possible effect of the quenched approximation.
