  We show that two P11 nucleon resonance poles near the pi Delta threshold,
obtained in several analyses, are stable against large variations of parameters
within a dynamical coupled-channels analysis based on meson-exchange
mechanisms. By also performing an analysis based on a model with a bare nucleon
state, we find that this two-pole structure is insensitive to the analytic
structure of the amplitude in the region below pi N threshold. Our results are
M_pole = (1363^{+9}_{-6} -i79^{+3}_{-5}) MeV and (1373^{+12}_{-10}
-i114^{+14}_{-9}) MeV. We also demonstrate that the number of poles in the 1.5
GeV < W < 2 GeV region could be more than one, depending on how the structure
of the single-energy solution of SAID is fitted. For three-pole solutions, our
best estimated result of a pole near N(1710) listed by Particle Data Group is
(1829^{+131}_{-65} -i192^{+88}_{-110}) MeV which is close to the results of
several previous analyses. Our results indicate the need of more accurate pi N
reaction data in the W > 1.6 GeV region for high precision resonance
extractions.
