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In this article, we consider the long-time behavior of solutions for the wave equation with nonlinear damping and linear memory. Within the theory of process on time-dependent spaces, we verify the process is asymptotically compact by using the contractive functions method, and then obtain the existence of the time-dependent attractor inH  0   1    (   Ω   )  ×   L   2    (   Ω   )  ×   L   μ    2    (    R    +    ;   H  0   1    (   Ω   )  )$\begin{array}{} H^{1}_0({\it\Omega})\times L^{2}({\it\Omega})\times L^{2}_{\mu}(\mathbb{R}^{+};H^{1}_0({\it\Omega})) \end{array}$   .

Time-dependent attractor of wave equations with nonlinear damping and linear memory