We explore the usefulness of the existing relations between the S-matrix and time delay in characterizing baryon resonances in pion–nucleon scattering. We draw attention to the fact that the existence of a positive maximum in time delay is a necessary criterion for the existence of a resonance and should be used as a constraint in conventional analyses which locate resonances from poles of the S-matrix and Argand diagrams. The usefulness of the time delay plots of resonances is demonstrated through a detailed analysis of the time delay in several partial waves of π N elastic scattering.