Experimental and theoretical investigations are reported of the E.S.R. spectroscopy of cyclooctatetraene (COT) and 1,3,5,7-tetramethylcyclooctatetraene (TMCOT) monoanion radicals oriented in single crystals of dialkali metal cyclooctatetraene diglyme (MzCOT. dg), Where M= K, Rb or Cs, and dipotassium 1,3,5,7-tetramethylcyclooctatetraene bis(diglyme) (K~TMCOT-2dg), respectively. Theoretical calculations are presented which explain why, as previously found experimentally, the equilibrium position of the COT monoanion in single crystals of M2COT. dg at low temperatures is rotated about its D 8 symmetry axis by an angle of 22.5 ~ relative to the equilibrium position of the COT dianion. Also presented are calculations of the ion-pair association energies (due to the electrostatic interactions of the nearest neighbour alkali metal ions and COT monoanion) which show that (a) the orbital degeneracy of the free, unperturbed COT monoanion is removed and (b) the lowest energy state of the COT monoanion (in agreement with experiment) is antisymmetric with respect to reflection through a mirror plane perpendicular to the COT molecular plane. Measurements of the values of the principal components of the g-tensor of the oriented COT monoanion are also reported. They show that only one component (gzz) is dependent upon temperature. These observations are contrasted with the situation for the TMCOT monoanion for which all three principal components of the g-tensor are found to be independent of temperature. Calculations of the values of the principal components of the g-tensor for the COT and TMCOT monoanions are presented. It is shown that, for the COT monoanion, the sign of the change in gzz with temperature, as well as the change itself, can be accounted for if interactions between the COT monoanion and the nearest neighbour alkali metal ions are explicitly taken into account.