For a smooth bounded domain \(\Omega \subset R^ n\), \(n\leq 3\), and \(\epsilon\) a real parameter, consider the hyperbolic equation \[ \epsilon u_{tt}+u_ t-\Delta u=-f(u)-g\quad in\quad \Omega \] with Dirichlet boundary conditions. Under certain conditions on the function f(u), this equation has a compact attractor \({\mathcal A}_{\epsilon}\) in \(H^ 1_ 0\times L^ 2\). For \(\epsilon =0\), the parabolic equation also has a compact attractor which can be naturally embedded into a compact set \({\mathcal A}_ 0\) in \(H^ 1_ 0\times L_ 2\). The authors demonstrate that, for any neighborhood of U, the set \({\mathcal A}_{\epsilon}\subset U\) for \(\epsilon\) small.