The general form of the cross section as well as the polarizations of electron-deuteron elastic scattering are given. Two-photon exchange effects are analyzed. Possible signatures of the two-photon exchange effects in the electron-deuteron elastic scattering are discussed. PACS: 13.40.GP, 25.30.-c, 25.30.Bf, 24.70.+s, 13.60.Fz