  The issue of the spin gap in the magnetic susceptibility $\chi''(q,\omega)$
in high T_c superconductors is discussed within a scenario of a mixture of
localized tightly bound electron pairs in singlet states (bi-polarons) and
itinerant electrons. Due to a local exchange between the two species of charge
carriers, antiferromagnetic correlations are induced amongst the itinerant
electrons in the vicinity of the sites containing the bound electron pairs. As
the temperature is lowered these exchange processes become spatially correlated
leading to a spin wave-like spectrum in the subsystem of the itinerant
electrons. The onset of such coherence is accompanied by the opening of a
pseudo gap in the density of states of the electron subsystem whose temperature
dependence is reflected in that of $\chi'' (q,\omega)$ near $q =(\pi,\pi)$
where a ``spin gap'' is observed by inelastic neutron scattering and NMR.
