We present inelastic neutron scattering measurements performed on thre
e La2-xSrxCuO4 high T-c single crystals, with x = 10%, 15% and 20% (T-
c= 25, 35 and 12K, respectively). We report here a complete study of t
he evolution of delta with doping providing evidence far a saturation
of delta in the overdoped regime. In addition, for x = 10%, while the
low energy magnetic fluctuations are clearly peaked at incommensurate
positions, the high energy response evolves back to the commensurate p
osition (pi,pi) and drops to the background above around 60 meV. Below
T-c, a 3.5 meV magnetic gap opens up for the optimaI doping is (x=15%
), while for the underdoped and overdoped crystals is (x=10% and 20%)
our experiment fails to reveal any significant magnetic gap above 1.2
meV and down to 1.5 K.