  We calculate the effects on the elastic electron-proton scattering cross
section of the two-photon exchange contribution with an intermediate $\Delta$
resonance. The $\Delta$ two-photon exchange contribution is found to be smaller
in magnitude than the previously evaluated nucleon contribution, with an
opposite sign at backward scattering angles. The sum of the nucleon and
$\Delta$ two-photon exchange corrections has an angular dependence compatible
with both the polarisation transfer and the Rosenbluth methods of measuring the
nucleon electromagnetic form factors.
