This paper is concerned with the first initial and boundary value problem of a class of nonclassical diffusion equations in solids. We first establish uniform decay estimates which are independent of the viscosity coefficient and prove some new existence and uniqueness results for solutions of the problem under some appropriate conditions. Then we show that it has a global pullback attractor. In the periodic case, we point out that the pullback attractor is actually periodic and forward attracting; furthermore, the problem has at least a periodic solution.