In this paper we study the existence of solutions for a coupled Allen-Cahn-Navier-Stokes model in two dimensions with an external force containing infinite delay effects in the weighted space Cδ(Y)\documentclass[12pt]{minimal}
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\begin{document}$C_{\delta }( \mathbb{Y})$\end{document}. We prove the existence of pullback attractors for the dynamical system associated to the problem under more general assumptions.