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Spin excitations of La2-xSrxCuO have been studied using inelastic neutron scattering techniques in the energy range of 2 meV =< w =< 12 meV and the temperature range of 8 K =< T =< 150 K. We observed a signature of a spin pseudo gap in the excitation spectrum above Tc for the slightly overdoped sample with x = 0.18. On heating, the spin pseudo gap gradually collapses between T = 80 K and 150 K. For the x = 0.15 and 0.20, although the visibility of gap-like structure at T ~ Tc is lower compared to the x = 0.18 sample, the broad bump of kai"(w) appears at w ~ 5 meV,close to the spin-gap energy at base temperature, suggests the existence of the spin pseudo gap in the normal state., Comment: revtex, 7 pages, 8 eps figures, PRB (2003) in press