  We present an analysis of a system of weakly coupled Hubbard chains based on
combining an exact study of spectral functions of the uncoupled chain system
with a renormalization group method for the coupled chains. For low values of
the onsite repulsion $U$ and of the doping $\delta$, the leading instability is
towards a superconducting state. The process includes excited states above a
small correlation pseudogap. Similar features appear in extended Hubbard models
in the vicinity of commensurate fillings. Our theoretical predictions are
consistent with the phase diagram observed in the (TMTTF)$_2$X and (TMTSF)$_2$X
series of organic compounds.
