  Recent inelastic neutron scattering (INS) experiments on
La$_{2-x}$Sr$_x$CuO$_4$ observed a {\it magnetic coherence effect}, i.e.,
strong frequency and momentum dependent changes of the spin susceptibility,
$\chi''$, in the superconducting phase. We show that this effect is a direct
consequence of changes in the damping of incommensurate antiferromagnetic spin
fluctuations due to the appearance of a d-wave gap in the fermionic spectrum.
Our theoretical results provide a quantitative explanation for the weak
momentum dependence of the observed spin-gap. Moreover, we predict {\bf (a)} a
Fermi surface in La$_{2-x}$Sr$_x$CuO$_4$ which is closed around $(\pi,\pi)$ up
to optimal doping, and {\bf (b)} similar changes in $\chi''$ for all cuprates
with an incommensurate magnetic response.
