A class of semilinear evolution equations of the second order in time of the form is considered, where is the Dirichlet Laplacian, is a smooth bounded domain in and . A local well posedness result is proved in the Banach spaces when satisfies appropriate critical growth conditions. In the Hilbert setting, if satisfies an additional dissipativeness condition, the nonlinear semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.