Vladimir Georgescu Spectral Analysis of Quantum Field Models with a Particle Number Cutoff (171K, Postscript) ABSTRACT. We determine the essential spectrum and prove the absence of singular continuous spectrum for a class of boson quantum field models with cutoffs. Our main purpose, however, is to show the power of an algebraic technique based on the study of the $C^*$-algebra generated by the operators which are natural candidates as hamiltonians of the system in a given physical situation.