  We consider two-photon exchange (TPE) in the elastic electron-proton
scattering and evaluate the effect of \pi N (pion + nucleon) intermediate
hadronic states. Among different \pi N states, we concentrate on the P33
channel; thus we effectively include Delta(1232) resonance with realistic width
and shape and corresponding background as well. In agreement with the previous
result, obtained for the zero-width resonance, we observe that the TPE
correction to the electric form factor is the largest one; it grows with Q^2
and at Q^2 > 2.5 GeV^2 exceeds the corresponding elastic contribution.
