  The effects of higher order coupling of surface vibrations to the relative
motion on heavy-ion fusion reactions at near-barrier energies are investigated.
The coupled channels equations are solved to all orders, and also in the linear
and the quadratic coupling approximations. It is shown that the shape of fusion
barrier distributions and the energy dependence of the average angular momentum
of the compound nucleus can significantly change when the higher order
couplings are included. The role of octupole vibrational excitation of ^{16}O
in the ^{16}O + ^{144}Sm fusion reaction is also discussed using the all order
coupled-channels equations.
