  The analytic properties of scattering amplitudes provide important
information. Besides the cuts, the poles and zeros on the different Riemann
sheets determine the global behavior of the amplitude on the physical axis.
Pole positions and residues allow for a parameterization of resonances in a
well-defined way, free of assumptions for the background and energy dependence
of the resonance part. This is a necessary condition to relate resonance
contributions in different reactions. In the present study, we determine the
pole structure of pion-nucleon scattering in an analytic model based on meson
exchange. For this, the sheet structure of the amplitude is determined. To show
the precision of the resonance extraction and discuss phenomena such as
resonance interference, we discuss the S11 amplitude in greater detail.
