  It is shown that the Luttinger liquid is unstable to arbitrarily small
transverse hopping. It becomes either a Fermi liquid or exhibits long-range
order at zero temperature. The crossover temperatures below which either
transverse coherent band motion or long-range order start to develop can be
finite even when spin and charge velocities differ. Explicit scaling relations
for the one-particle and two-particle crossover temperatures are derived in
terms of transverse hopping amplitude, spin and charge velocities as well as
anomalous exponents. The special case of infinite-range transverse hopping can
be treated exactly and yields a Fermi liquid down to zero temperature, unless
the anomalous exponent $\theta $ is larger than unity.
