The analysis of the JLab proton polarization data on the ratio µpGEp(t)/GMp(t) in the framework of the unitary and analytic model of nucleon electromagnetic structure implicates surprising nondipole behavior of the proton electric form factor GEp(t) in the space-like region with the zero around the momentum transfer squared value t=-Q2=-13 GeV2. This result differs from the unpolarized cross-section measurements giving the dipole behavior of GEp(t) by means of the Rosenbluth technique. Recent investigations demonstrate that inclusion of a two-photon mechanism could solve the problem, which plays an important role for the unpolarized cross section, but it is negligible for the polarization ratio. Here, investigating a size of a difference in a prediction of the deuteron elastic structure functions A(t),B(t) by both, the nondipole and the old dipole, behaviors of GEp(t) in space-like region through the nonrelativistic impulse approximation, we have come to the conclusion that the two-photon mechanism plays much less of a role for the unpolarized electron-deuteron elastic scattering than for the unpolarized electron-proton elastic scattering.