  We present a general method for determining the phase diagram of systems of a
finite number of one dimensional Hubbard--like systems coupled by
single--particle hopping with weak interactions. The technique is illustrated
by detailed calculations for the two--chain Hubbard model, providing the first
controlled results for arbitrary doping and inter-chain hopping. Of nine
possible states which could occur in such a spin--$1/2$ ladder, we find seven
at weak coupling. We discuss the conditions under which the model can be
regarded as a one--dimensional analog of a superconductor.

Condensed Matter