Study of the NLSP from the GMSB models in the CMS detector at the LHC

Within Gauge-Mediated Supersymmetry Breaking ( GMSB) models gravitino is the Lightest Supersymmetry Partner ( LSP) whereas neutralino or stau plays the role of the Next to Lightest Supersymmetry Partner ( NLSP). NLSP decays to its Standard Model partner and gravitino with a lifetime depending on the scale of the SUSY breaking. Detection of the NLSP and determination of its properties, lifetime in particular can be of crucial importance for the physics program at LHC. We concentrate on two scenarios specific from the detection point of view. In the first long-lived stau is the NLSP, in the second decaying in flight neutralino is the NLSP. In the first case we show that CMS muon system is able to detect stau, determine its mass and put lower limit on the stau lifetime via time of flight measurement. Within this scenario discovery of supersymmetry turns out to be possible up to gluino andsquark masses of the order of 4~TeV. In the second case we use not pointing to the main vertex gammas recorded by the CMS electromagnetic calorimeter and a late electromagnetic showers detected in the CMS muon system to identify decaying in flight neutralinos. We comment on the possibility of mass and lifetime determination for such neutralino, and visibility of a short lived NLSP in the CMS detector.