  We have measured the beam-normal single-spin asymmetries in elastic
scattering of transversely polarized electrons from the proton, and performed
the first measurement in quasi-elastic scattering on the deuteron, at backward
angles (lab scattering angle of 108 degrees) for Q2 = 0.22 GeV^2/c^2 and 0.63
GeV^2/c^2 at beam energies of 362 MeV and 687 MeV, respectively. The asymmetry
arises due to the imaginary part of the interference of the two-photon exchange
amplitude with that of single photon exchange. Results for the proton are
consistent with a model calculation which includes inelastic intermediate
hadronic (piN) states. An estimate of the beam-normal single-spin asymmetry for
the scattering from the neutron is made using a quasi-static deuterium
approximation, and is also in agreement with theory.
