Bonding at stoichiometry and away from stoichiometry in binary ordered non-crystalline semiconductors is classified into covalent, ionic and metallic types. The composition dependence of their transport properties is shown to depend principally on the bonding configuration of any excess of a constituent beyond stoichiometry (compensated covalent, dative covalent or ionic) and not on whether the bonding at stoichiometry itself is covalent or ionic. Band models are introduced which explain the composition dependence of transport and optical properties of CsAu, GaAs, MgBi, MgSb, LiPb, CsSb, GaTe, GeTe and PbTe alloys. It is suggested that substitutional doping might be observable in a-GaP or a-GaAs over a small range of off-stoichiometric compositions. The group-IV chalcogenides show examples of both compensated covalent responses (for example, GeTe) and doped, ionic responses (for example, PbTe), depending on ionicity. It is proposed that in non-crystalline phases a critical value of covalent gap separates those systems existing in a 4 : 2 coordinated SiO2-like covalent structure from those with an ionic PbTe-type structure.