Abstract: We first proved the wellposedness of weak solutions for the nonclassical diffusion equations with time delays by using the FaedoGalerkin method, and then we gave  the pullback Dasymptotic compactness  by using the  contraction function method, which proved the existence of timedependent pullback attractor.

Key words: nonclassical diffusion equation, timedependent pullback attractor, pullback absorbing set, pullback