Magnesium Oxide crystals doped with chromium and cobalt have been investigated by optical spectroscopy and electron spin resonance spectroscopy. The optical work has provided information about the oxidation state and lattice site of the dopant ions, whilst the magnetic resonance results have given insight into the experience interactions between them. The Optical work on MgO:Cr has confirmed that the majority of dopant enters the lattice substitutionally as Cr3-*'up to I5IOO p.p.m., although at the higher concentration samples show evidence for a small amount of a second phase being formed. This has tentatively been ascribed as the spinel structure MgCr(_2)o(_4). A linewidth analysis of the electron spin resonance signal due to the even isotopes of Cr(^3+) in substitutional sites has been made at room temperature. The value of linewidth is found to be considerably less than predicted by Van Vleck's second moment theory, and furthermore is independent of concentration as opposed to the (concentration)(^½) dependance expected from this theory. The discrepancy has been explained on the grounds of a strong exchange field between the chromic ions which gives rise to exchange narrowing. This idea is supported by the coefficients of 1-nirtosis for the absorption lines which indicate a substantial trend to the Lorentsian lineshape. The strength of the exchange field has been measured as 4.45 X 10(^12) Hz from the e.s.r, data at both 9.3155 GHz and 35.5 GHz. A similar course of study was adopted for MgO:Co, Optical spectroscopy at both room and liquid nitrogen temperatures has shown that when discussing the 24-optical energy levels of Co substitutional in MgO considerable attention must be payed to spin-orbit coupling. The linewidth of the e.s.r. spectrum of this Co(^2+) taken at 9.5155 GHz between 4.2 and 65 K showed the linewidth to be a function of both temperature and concentration. The temperature dependance is attributed to a change in relaxation mechanism, and it is postulated that the Orbach process dominates above about utilising the first excited state of the spin orbit coupling levels, An attempt to factor off the temperature dependence of the linewidth has been made and again strong evidence for exchange narrowing, both from linewidth and lineshape arguments is seen. The strength of the exchange field has been calculated as 4.53 x 10(^12) Hz. Finally some previously published results for iron have been examined. From these the corresponding exchange field for Fe(^3+) in MgO has been evaluated as 1.14 x l0(^13) Hz
