In this paper, a class of Navier–Stokes equations with infinite delay is considered. It includes delays in the convective and the forcing terms. We discuss the existence of mild and classical solutions for the problem. We establish the results for an abstract delay problem by using the fact that the Stokes operator is the infinitesimal generator of an analytic semigroup of bounded linear operators. Finally, we apply these abstract results to our particular situation.944840855Caraballo, T., Real, J., Navier–Stokes equations with delays (2001) Proc. R. Soc. A, 457, pp. 2441-2453Caraballo, T., Real, J., Asymptotic behaviour of two-dimensional Navier-Stokes equations with delays (2003) Proc. R. Soc. A, 459, pp. 3181-3194Caraballo, T., Real, J., Attractors for 2D-Navier-Stokes models with delays (2004) J. Differ. Equ, 205, pp. 271-297Marín-Rubio, P., Real, J., Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators (2010) Discrete Contin. Dyn. Syst, 26, pp. 989-1006Taniguchi, T., The exponential behavior of Navier-Stokes equations with time delay external force (2005) Discrete Contin. Dyn. Syst, 12, pp. 997-1018Liu, X., Wang, Y., Pullback attractors for nonautonomous 2D-Navier-Stokes models with variable delays (2013) Abstr. Appl. Anal, 2013, p. 10 p. , Article ID 425031Garrido-Atienza, M.J., Marín-Rubio, P., Navier-Stokes equations with delays on infinite domains (2006) Nonlinear Anal, 64, pp. 1100-1118Marín-Rubio, P., Real, J., Attractors for 2D-Navier-Stokes equations with delays on some unbounded domains (2007) Nonlinear Anal, 67, pp. 2784-2799Niche, C.J., Planas, G., Existence and decay of solutions in full space to Navier-Stokes equations with delays (2011) Nonlinear Anal, 74, pp. 244-256Liu, W., Asymptotic behavior of solutions of time-delayed Burgers’ equation (2002) Discrete Contin. Dyn. Syst. Ser. B, 2, pp. 47-56Tang, Y., Wan, M., A remark on exponential stability of time-delayed Burgers equation (2009) Discrete Contin. Dyn. Syst. Ser. B, 12, pp. 219-225Planas, G., Hernández, E., Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations (2008) Discrete Contin. Dyn. Syst, 21, pp. 1245-1258Guzzo, S.M., Planas, G., On a class of three dimensional Navier-Stokes equations with bounded delay (2011) Discrete Contin. Dyn. Syst. Ser. B, 16, pp. 225-238Marín-Rubio, P., Real, J., Valero, J., Pullback attractors for a two-dimensional Navier-Stokes model in an infinite delay case (2011) Nonlinear Anal, 74, pp. 2012-2030Rankin, S.M., III, Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations (1993) Trans. Amer. Math. Soc, 336, pp. 523-535Caraballo, T., Kloeden, P.E., Real, J., Unique strong solutions and V-attractors of a three dimensional system of globally modified Navier-Stokes equations (2006) Adv. Nonlinear Stud, 6, pp. 411-436Kloeden, P.E., Caraballo, T., Langa, J.A., Real, J., Valero, J., The three-dimensional globally modified Navier-Stokes equations (2009) Mathematical problems in engineering aerospace and sciences, 3, pp. 11-22. , Sivasundaram S, Devi JV, Drici Z, McRae F, (eds), Cambridge: Cambridge Scientific PublishersKloeden, P.E., Marín-Rubio, P., Real, J., Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified Navier-Stokes equations (2009) Commun. Pure Appl. Anal, 8, pp. 785-802Romito, M., The uniqueness of weak solutions of the globally modified Navier-Stokes equations (2009) Adv. Nonlinear Stud, 9, pp. 425-427Marín-Rubio, P., Márquez-Durán, A.M., Real, J., On the convergence of solutions of globally modified Navier-Stokes equations with delays to solutions of Navier-Stokes equations with delays (2011) Adv. Nonlinear Stud, 11, pp. 917-927Caraballo, T., Márquez-Durán, A.M., Real, J., Pullback and forward attractors for a 3D LANS-α model with delay (2006) Discrete Contin. Dyn. Syst. Ser. A, 15, pp. 559-578Caraballo, T., Márquez-Durán, A.M., Real, J., Asymptotic behaviour of the three-dimensional α-Navier-Stokes model with delays (2008) J. Math. Anal. Appl, 340, pp. 410-423Caraballo, T., Márquez-Durán, A.M., Real, J., Asymptotic behaviour of the three-dimensional α-Navier-Stokes model with locally Lipschitz delay forcing term (2009) Nonlinear Anal, 71, pp. e271-e282Niche, C.J., Planas, G., Existence and decay of solutions to the dissipative quasi-geostrophic equation with delays (2012) Nonlinear Anal, 75, pp. 3936-3950Tachim-Medjo, T., Attractors for the multilayer quasi-geostrophic equations of the ocean with delays (2008) Appl. Anal, 87, pp. 325-347Tachim-Medjo, T., Multi-layer quasi-geostropic equations of the ocean with delays (2008) Discrete Contin. Dyn. Syst. Ser. B, 10, pp. 171-196Tachim-Medjo, T., The primitive equations of the ocean with delays (2009) Nonlinear Anal. Real World Appl, 10, pp. 779-797Wan, L., Duan, J., Exponential stability of the multi-layer quasi-geostrophic ocean model with delays (2009) Nonlinear Anal, 71, pp. 799-811Fujiwara, D., Morimoto, H., An Lp theorem of the Helmholtz decomposition of vector fields (1977) J. Fac. Sci. Univ. Tokyo Sect. Math. IA, 24, pp. 685-700Giga, Y., Analyticity of the semi-group generated by the Stokes operator in Lp spaces (1981) Math. Z, 178, pp. 297-329Giga, Y., Domains of fractional powers of the Stokes operator in Lp spaces (1985) Arch. Ration. Mech. Anal, 89, pp. 251-265Bridges, T.J., The Hopf bifurcation with symmetry for the Navier-Stokes equations in (Lp(Ω))n, with application to plane Poiseuille flow (1989) Arch. Ration. Mech. Anal, 106, pp. 335-376Hino, Y., Murakami, S., Naito, T., (1991) Lecture notes in mathematics, 1473. , Berlin: Springer-VerlagHenríquez, H.R., Regularity of solutions of abstract retarded functional-differential equations with unbounded delay (1997) Nonlinear Anal, 28, pp. 513-531