[en] We study both the branching ratio for b→sγ decay and the muon anomalous magnetic moment, a_μ≡(g-2)_μ/2, in the minimal supersymmetric standard model with gauge-mediated supersymmetry breaking. Combining new experimental data on a_μ and the branching ratio for b→sγ, strong limits on the parameter space of these models are derived. We find that this combined study leads to much stronger constraints on the parameter space of the model than those from either b→sγ or a_μ. In particular, the region of large tan β is extremely limited, which would have been otherwise allowed. We include the supersymmetric one-loop correction to the mass of b quark, m_b, and find that in order to have a correct value of m_b, the region of large tan β and μ<0 (in our convention) is not allowed in these models. The region of large tan β and μ>0 is also strongly constrained. We present bounds on supersymmetric particle masses as a function of tan β. (c) 2000 The American Physical Society