Higgs singlet superfields are usually present in most extensions of the Minimal Supersymmetric Standard Model (MSSM) that address the mu-problem, such as the Next-to-Minimal Supersymmetric Standard Model (NMSSM) and the Minimal Nonminimal Supersymmetric Standard Model (MNSSM). Employing a gauge- and flavour-covariant effective Lagrangian formalism, we show how the singlet Higgs bosons of such theories can have significant contributions to B-meson flavour-changing neutral current (FCNC) observables for large values of $tanbeta stackrel{>}{{}_sim} 50$ at the 1-loop level. Illustrative results are presented including effects on the B_s and B_d mass differences and on the rare decay $B_stomu^+mu^-$. In particular, we find that depending on the actual value of the lightest singlet pseudoscalar mass in the NMSSM, the branching ratio for $B_stomu^+mu^-$ can be enhanced or even suppressed with respect to the Standard Model prediction by more than one order of magnitude.
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