ABSTRACTIn this paper, we consider the asymptotic behavior of weak solutions for nonclassical nonautonomous diffusion equations with a delay operator in time‐dependent spaces when the nonlinear function satisfies subcritical exponent growth conditions, the delay operator contains some hereditary characteristics, and the external force . First, we prove the well‐posedness of solutions by using the Faedo–Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time‐dependent spaces and , respectively.