This paper (the second in a series) reports our recent progress in the study of strong-coupling quantum field theories on a lattice. In particular we study theories involving fermions and gauge fields and pay special attention to the peculiar problems encountered when one formulates theories of fermions on a lattice. It is unique to our approach that we preserve local chiral symmetry and at the same time correctly count the number of fermionic states. We demonstrate how our formalism works with the lattice Thirring and Schwinger models, whose continuum limits are solvable in one space and one time dimension. We show in the strong-coupling limit that these theories are equivalent to a Heisenberg antiferromagnetic chain. We also discuss briefly some general features of non-Abelian gauge theories of quarks and gluons in three space and one time dimension. The most interesting results we have to report at this stage are as follows: (i) The only "gauge-invariant states" which remain at low mass in the limit of very strong gauge coupling have the quantum numbers of physical hadrons. (ii) The resulting "effective strong-coupling" theory preserves the full chiral symmetry of the exact theory [SU(3) × SU(3) if we introduce three flavors of quarks each with three colors] and describes a theory of "massless bare hadrons" interacting with one another through a quark interchange mechanism of finite strength.