  We derive a Nambu--Jona-Lasinio (NJL) model from a non-local gauge theory and
show that it has confining properties at low energies. In particular, we
present an extended approach to non-local QCD and a complete revision of the
technique of Bender, Milton and Savage applied to non-local theories, providing
a set of Dyson--Schwinger equations in differential form. In the local case, we
obtain closed form solutions in the simplest case of the scalar field and
extend it to the Yang--Mills field. In general, for non-local theories, we use
a perturbative technique and a Fourier series and show how higher-order
harmonics are heavily damped due to the presence of the non-local factor. The
spectrum of the theory is analysed for the non-local Yang--Mills sector and
found to be in agreement with the local results on the lattice in the limit of
the non-locality mass parameter running to infinity. In the non-local case, we
confine ourselves to a non-locality mass that is sufficiently large compared to
the mass scale arising from the integration of the Dyson--Schwinger equations.
Such a choice results in good agreement, in the proper limit, with the spectrum
of the local theory. We derive the gap equation for the fermions in the theory
that gives some indication of quark confinement in the non-local NJL case as
well. Confinement seems to be a rather ubiquitous effect that removes some
degrees of freedom in the original action, favouring the appearance of new
observable states, as seen, e.g.,\ for quantum chromodynamics at lower
energies.
