The status of two on-going studies concerning important aspects of the phenomenology of gauge-mediated supersymmetry breaking (GMSB) models at TeV colliders is reported. The first study deals with the characteristics of the light Higgs boson spectrum allowed by the (minimal and non-minimal) GMSB framework. Todays most accurate GMSB model generation and two-loop Feynman-diagrammatic calculation of m_h have been combined. The Higgs masses are shown in dependence of various model parameters at the messenger and electroweak scales. In the minimal model, an upper limit on m_h of about 124 GeV is found for m_t = 175 GeV. The second study is focused on the measurement of the fundamental SUSY breaking scale sqrt(F) at the LHC in the GMSB scenario where a stau is the next-to-lightest SUSY particle (NLSP) and decays into a gravitino with c*tau_NLSP in the range 0.5 m to 1 km. This implies the measurement of mass and lifetime of long lived sleptons. The identification is performed by determining the time of flight in the ATLAS muon chambers. Accessible range and precision on sqrt(F) achievable with a counting method are assessed.
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