  We calculate two-photon exchange amplitudes for the elastic electron-hadron
scattering in the nonrelativistic approximation, and obtain analytical formulae
for them. Numerical calculations are performed for proton and $^3$He targets.
Comparing our numerical results with relativistic calculations, we find that
the real part of the amplitude is described well at moderate $Q^2$, but the
imaginary part strongly differs from the relativistic result. Thus the
nonrelativistic approximation should not be used for calculation of observables
which depend on the imaginary part of the amplitude, such as single-spin
asymmetries.
