  We study the effects of phonons in $N$-leg Hubbard ladders within the
framework of a one-loop renormalization group. In particular, we explicitly
demonstrate that the role of phonons changes {\em qualitatively} even in the
simplest two-leg ladder, as compared to the single-chain system where phonons
always dominate. Our numerical results suggest that in the spin-gapped phase of
the two-leg ladder, the opening of the spin gap by electron-electron
interaction also drives the electron-phonon interaction to strong coupling, but
in a {\em subdominant} fashion. Therefore, even though the inclusion of phonons
does not alter the phase, their subdominant relevance strongly renormalizes
some physical properties below the energy scale of the spin gap. This might
shine some light on the recent experiments showing an anomalous isotope effects
in high-temperature superconductors.
