Nuclear spin exchange in the ionic clusters [Tl4Cl](3+), situated in t
he cavities of cation-substituted chlorosodalite, was investigated by
the Tl-203 and Tl-205 NMR method. It was shown that nuclear spin excha
nge in the ionic crystals is realized by analogy with the Kramers mech
anism of indirect exchange of electron spins using the electron shells
of the bridging atoms.