Relativistic and non-relativistic Hartree–Fock one-centre expansion calculations are reported for the linear systems MH+ and MH2(M = Be, Mg, Ca, Sr, Ba, Ra, Zn, Cd, Hg, Yb, No). Previous results for CuH, AgH and AuH are refined. Strong d orbital contributions and consequently very small relativistic bond length contractions, C, are found for the heavier alkaline earths. The d character increases monotonically along the series Be, Mg, Ca, Sr, Ba but drops back, due to relativistic effects, for Ra. For Zn, Cd and Hg larger C values of ≈ 1, 2 and 7% are found. “Molecular” covalent radii, consistent with Pauling's halogen radii, are deduced for all the elements considered. The corresponding radii for hydrogen and carbon, bound to them, are discussed. Bond lengths of the unknown species CaH+, SrH+, BaH+, RaH+ and YbH+ are predicted to be 193, 210, 227, 240 and 202 pm, respectively. The radii of No and Yb are found to be comparable, in agreement with experiment. The lanthanoid and actinoid contractions are discussed. Nyholm's explanation of the linear coordination of Hg as being due to a large s–p separation is ascribed to relativistic effects.