It is shown that the influence of the local environment on the KLV Auger spectra of Mg can be understood via a theoretical approach which uses the embedding technique to calculate the local density of states around a core-ionized Mg site. This approach is applied to Al₈₅Mg₁₅, Mg₁₀₀ and Li₈₅Mg₁₅, providing matrix element effects are included, the results obtained are in good agreement with measurements of the KL₁V Auger profiles for these material. The approach is less successful for the Mg KL_2,3V transitions. The theoretical study predicts the formation of a bound state of s character on the Mg site in Li₈₅Mg₁₅ and this is supported by the good agreement obtained between theoretical and experimental KL₁V Auger lineshapes.