We study the semileptonic decays B --> X(s)e(+)e(-), B --> X(s)mu(+)mu(-) i
n generic supersymmetric extensions of the Standard Model. SUSY effects are
parameterized using the mass insertion approximation formalism and differe
nces with the Constrained MSSM results are pointed out. Constraints on SUSY
contributions coming from other processes (e.g. b --> s gamma) are taken i
nto account. Chargino and gluino contributions to photon and Z-mediated dec
ays are computed and non-perturbative corrections are considered. We find t
hat the integrated branching ratios and the asymmetries can be strongly mod
ified. Moreover, the behavior of the differential forward-backward asymmetr
y remarkably changes with respect to the Standard Model expectation. (C) 20
00 Elsevier Science B.V. All rights reserved.