We have analyzed Coulomb drag between currents of interacting electrons in
two parallel one-dimensional conductors of finite length L attached to exte
rnal reservoirs. For strong coupling, the relative fluctuations of electron
density in the conductors acquire energy gap M. At energies larger than Ga
mma = const X nu- exp(-LM/nu-)/L + Gamma (+), where Gamma (+) is the impuri
ty scattering rate, and, for L > nu-/M, where nu- is the fluctuation veloci
ty, the gap leads to an "ideal" drag with almost equal currents in the cond
uctors. At low energies the drag is suppressed by coherent instanton tunnel
ing, and the zero-temperature transconductance vanishes, indicating the Fer
mi-liquid behavior.