A model suspension of diffusing spherical particles with an internal degree of freedom taking two discrete values, or equivalently a two-component suspension with reactions between species, is studied. The internal degrees of freedom of neighboring particles are coupled by an Ising type interaction of short range. The dynamics of the Ising variables is described by a master operator of Glauber form. On a macroscopic level small deviations of the two densities from their equilibrium averages obey transport equations with memory character. The memory kernel is derived from the Mori formalism. The two-body contribution to the cluster expansion of the memory function is obtained analytically at zero wavevector. The spectrum of the memory function shows a marked dependence on the presence or absence of an external field, the ratio of time scales for transitions between states and for translational diffusion, and on the antiferromagnetic or ferromagnetic character of the Ising interaction.