<p>We investigate fast space-time solvers for two approaches of space-time finite element methods for the wave equation in second-order formulation. The first approach is of continuous Galerkin–Petrov type using a stabilization, while the second one is of continuous Galerkin–Bubnov type based on the new modified Hilbert transformation. Both finite element methods are of tensor-product type and allow for arbitrary polynomial degrees in space and time. However, these space-time methods lead to huge linear systems. In this work, we develop and analyze fast direct solution techniques, which are based on the Bartels–Stewart method and the fast diagonalization method. All proposed space-time solvers result in a sequence of spatial subproblems. The solvers, based on the fast diagonalization method, allow for time parallelization by solving the spatial subproblems in parallel. It turns out that the fast diagonalization method is only conditionally applicable to the Galerkin–Petrov method, i.e., uniform time meshes are not allowed. However, for the Galerkin–Bubnov method uniform time meshes are perfectly suited, i.e., time parallelization is possible. We analyze all steps of the proposed algorithms including complexity estimates. Moreover, for all developed space-time solvers using sparse direct solvers for the spatial subproblems, we show a series of numerical experiments, where we focus on a spatially two-dimensional domain. These experiments confirm the theoretical findings.</p>