A theoretical study is performed of the H-1 relaxation behavior of an organic molecule that is adsorbed in a zeolite exchanged with transition metal ions. An expression is derived for the spin-lattice and spin-spin relaxation rate constant of a uniform proton ensemble, while the occurrence of molecular exchange is taken into account. The influence is analyzed of an approach of a uniform proton ensemble toward the nearest neighboring paramagnetic ion system. It is shown that there exists a signal extinction effect, for which the critical distance was estimated.