  The existence of traveling and standing waves is investigated for chains of
coupled pendula with periodic boundary conditions. The results are proven by
applying topological methods to subspaces of symmetric solutions. The main
advantage of this approach comes from the fact that only properties of the
linearized forces are required. This allows to cover a wide range of models
such as Newton's cradle, the Fermi-Pasta-Ulam lattice and the Toda lattice.
