Results of extensive Cu NMR and NQR studies in the superconducting La2
-xSrxCuO4 with x=0.075-0.24 have been presented. The rapid decrease of
the nuclear spin-lattice relaxation rate, 1/T1, and the spin Knight s
hift below T(c) confirm microscopically the existence of the supercond
ucting phase with lower T(c) than 38 K for 0.10 less-than-or-equal-to
x less-than-or-equal-to 0.24. For x = 0.10, magnetic anomalies emerge
at low-T in some small parts of the sample, e.g. T-independent T1 and
broadening of spectrum, having some relevance to the magnetic order in
La2 BaxCuO4 with x = 0.125. For x>0.15, the T1T = const. behavior and
the existence of the residual spin Knight shift far below T(c) have r
evealed that the superconductivity is of a gapless type with a finite
density of states at the Fermi level caused by the mixture of differen
t structures, i.e. tetragonal and orthorhombic.