MPEJ Volume 9, No. 1, 15 pp. Received: Feb 28, 2003. Accepted: Apr 14, 2003. Paolo Perfetti A KAM theorem for infinite--dimensional discrete systems ABSTRACT: Infinite--dimensional, discrete hamiltonian systems of the type kinetic energy + potential energy over ${\Bbb R}^{{\Bbb Z}}\times {\Bbb T}^{{\Bbb Z}}$ are studied. The existence of many quasi--periodic motions with a maximal set of nonzero frequencies is shown. http://www.maia.ub.es/mpej/Vol/9/1.ps http://www.ma.utexas.edu/mpej/Vol/9/1.ps http://mpej.unige.ch/mpej/Vol/9/1.ps