In the spirit of a statistical approach to theS-matrix, we discuss the concept of resonant state and we are led to generalize the eigenphase formalism to many-particle processes. We show that the object to be considered is the connected part of theS-matrix at fixed total four-momentum and we give strong arguments in favour of the conjecture that this operator is compact. This enables us to write a generalized eigenfunction expansion. We define a « structure function » which describes the distribution of the eigenvalues and we study some of its general properties. We consider also some consequences of the assumption that the amplitude is dominated by resonances.