The original Fermi-Pasta-Ulam (FPU) problem considers a chain of N so-called monoatomic elements, i.e. all masses equal. The idea of the model was to demonstrate the statistical mechanics phenomenon of equipartition of energy. However, the system does show recurrence phenomena, even for a large number of particles. From averaging-normalisation we find generically in FPU chains invariant submanifolds that have a remarkable impact on the dynamics. Also it is possible to prove an embedding theorem that relates the behaviour of an FPU chain with n particles with a chain that contains an arbitrary multiple of n particles. FPU chains with unequal masses can produce very different resonance problems. Interesting cases are chains with alternating masses where even significant interactions between small and large masses are possible.