We extend the results of Mirabelli and Peskin to supergravity. We study the compactification on S-1/Z(2) of Zucker's off-shell formulation of 5D supergravity and its coupling to matter at the fixed points. We clarify some issues related to the off-shell description of supersymmetry breaking a la Scherk-Schwarz (here employed only as a tool), discussing how to deal with singular gravitino wave functions. We then consider 'visible' and 'hidden' chiral superfields localized at the two different fixed points and communicating only through 5D supergravity. We compute the one-loop corrections that mix the two sectors and the radion superfield. Locality in 5D ensures the calculability of these effects, which transmit supersymmetry breaking from the hidden to the visible sector. In the minimal set-up visible-sector scalars get a universal squared mass m(0)(2) < 0. In general (e.g., in the presence of a sizeable gravitational kinetic term localized on the hidden brane) the radion-mediated contribution to m(0)(2) can be positive and dominant. Although we did not build a complete satisfactory model, brane-to-brane effects can cure the tachyonic sleptons predicted by anomaly mediation by adding a positive m(0)(2), which is universal up to subleading flavour-breaking corrections. (C) 2003 Elsevier B.V. All rights reserved.