Bruno Nachtergaele, Hillel Raz, Benjamin Schlein, Robert Sims Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems (78K, LateX) ABSTRACT. We prove Lieb-Robinson bounds for systems defined on infinite dimensional Hilbert spaces and described by unbounded Hamiltonians. In particular, we consider harmonic and certain anharmonic lattice systems.