  We calculate the fermion Green function and particle-hole susceptibilities
for a degenerate two-dimensional fermion system with a singular gauge
interaction. We show that this is a strong coupling problem, with no small
parameter other than the fermion spin degeneracy, N. We consider two
interactions, one arising in the context of the $t-J$ model and the other in
the theory of half-filled Landau level. For the fermion self energy we show in
contrast to previous claims that the qualitative behavior found in the leading
order of perturbation theory is preserved to all orders in the interaction. The
susceptibility $\chi_Q$ at a general wavevector $\bf{Q} \neq 2\bf{p_F}$ retains
the fermi-liquid form. However the $2p_F$ susceptibility $\chi_{2p_F}$ either
diverges as $T -> 0$ or remains finite but with nonanalytic wavevector,
frequency and temperature dependence. We express our results in the language of
recently discussed scaling theories, give the fixed-point action, and show that
at this fixed point the fermion-gauge-field interaction is marginal in $d=2$,
but irrelevant at low energies in $d \ge 2$.
