Recent inelastic-neutron-scattering experiments on La2-xSrxCuO4 observed a
magnetic coherence effect, i.e., strong frequency- and momentum-dependent c
hanges of the spin susceptibility, chi", in the superconducting phase. We s
how that this effect is a direct consequence of changes in the damping of i
ncommensurate antiferromagnetic spin fluctuations due to the appearance of
a d-wave gap in the fermionic spectrum. Our theoretical results provide a q
uantitative explanation for the weak momentum dependence of the observed sp
in gap. Moreover, we predict (a) a Fermi surface in La2-xSrxCuO4 which is c
losed around (pi, pi) up to optimal doping and (b) similar changes in chi"
for all cuprates with an incommensurate magnetic response.