Integral cross sections for fission and for one-and two-neutron transfer reactions in the system ~ 32Xe + 23sU were measured radiochemically in the energy range 0.7 < E/Ecou~ < 1. The excitation functions for fission and transfer are found to be essentially parallel below 0.85 x Ecou~. Even at the lowest energies the transfer cross sections exceed the fission cross section by more than one order of magnitude. With the other projectiles 129Xe and 136Xe different transfer cross sections illustrating their sensitivity for the ground state Qvalues, Qg~, are observed while the fission cross sections are the same as in the 132Xe +23Su reaction. The fission data are interpreted in terms of a continuous transition between Coulomb fission and several transfer-induced fission processes.