  We analyze the problem of Luttinger liquids coupled via a single-particle
hopping $\tp$ and introduce a systematic diagrammatic expansion in powers of
$\tp$. An analysis of the scaling of the diagrams at each order allows us to
determine the power-law behavior versus $\tp$ of the interchain hopping and of
the Fermi surface warp. In particular, for strong interactions, we find that
the exponents are dominated by higher-order diagrams producing an enhanced
coherence and a failure of linear-response theory. Our results are valid at any
finite order in $\tp$ for the self-energy.
