<p>This paper is devoted to the study of a class of reaction diffusion difference systems with distributed delay and a non monotone nonlinearity admitting three equilibria, those types of nonlinearities are famously known as bistable nonlinearities. We describe the asymptotic behaviour of solutions of such problems, and we prove that according to the initial data, the trivial and the second steady state are attractive. This implies naturally that the first steady state is not stable. The fact that the nonlinearity is not monotone makes it difficult to use a direct sub-and supersolution argument, therefore we adapt an adequate method. To our knowledge, this is the first time where such types of general systems are studied.</p>