B -> X-s gamma in supersymmetry: large contributions beyond the leading order

We discuss possible large contributions to B --> X(s)gamma, which can occur at the next-to-leading order in supersymmetric models. They can originate from terms enhanced by tan fi factors, when the ratio between the two Higgs vacuum expectation values is large, or by logarithm of M-SUSY/M-W, when the supersymmetric particles are considerably heavier than the W boson. We give compact formulae which include all potentially large higher-order contributions. We find that tan fi terms at the next-to-leading order do not only appear from the Hall-Rattazzi-Sarid effect (the modified relation between the bottom mass and Yukawa coupling), but also from an analogous effect in the top-quark Yukawa coupling. Finally, we show how next-to-leading order corrections, in the large tan beta region, can significantly reduce the limit on the charged-Higgs mass, even if supersymmetric particles are very heavy.