The problem of bidirectionality in bianisotropic media, i.e. existence of plane eigenwaves propagating forwards and backwards along a certain direction with the same propagation factor is discussed. It is shown that bidirectionality in bianisotropic media exists for the following directions: (1) perpendicular to a plane of symmetry, (2) perpendicular to a proper axis, (3) along an improper axis, (4) parallel to an antiplane, (5) along an antiaxis of symmetry.