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This thesis investigates the incorporation and solubility behaviour of three anionic species (sulphate, chloride and molybdate) in two different types of glasses (borosilicate and aluminosilicate glasses). These anions can be often found in nuclear waste and their poor solubilities in nuclear waste glasses are a main factor that controls the loading capacity of nuclear waste vitrification. The investigations in this thesis are therefore focused on the compositional dependence of their solubilities in glass, together with the effects of their incorporations on glass structure and properties. A variety of glass properties have been assessed. Glass densities steadily increased with increasing incorporation of sulphate and molybdate but showed maxima with chloride incorporation. Glass transition temperatures Tg all decreased with initial anionic loadings, whereas further loadings results in either decreased or unchanged Tg depending on anionic species and glass composition. Intense Raman peaks are created due to sulphate and molybdate additions; these characteristic peaks are assigned to the vibrations of SO42– and MoO42–, respectively. The shift of these peaks with variation of alkaline earth species in glass suggests the association of SO42– and MoO42– with alkaline earth cations in glass network. The incorporation of chloride does not cause significant changes in the Raman spectra, however. Based on X-ray diffraction results the visibly homogeneous glasses were completely amorphous while the phase separated glasses contained a number of crystals. There are two mechanisms of phase separation occurring in the glasses with excess sulphate and molybdate: liquid-liquid separation and thereafter crystallisation, which occurs during cooling within glass melts with critical amounts of sulphate or molybdate; or a segregated layer, which occurs if the addition of sulphate or molybdate is too excessive to be completely dissolved in the melt. The crystals formed through the former mechanism are mostly spherical, submicron in size and randomly dispersed. These crystals are more likely to be alkaline earth salts while the segregated layers are essentially sodium salts. The phase separation caused by excess chloride in melt is different. The separated phases in aluminosilicate glasses are all non-chlorine containing and are formed through nucleation and growth during cooling. Sulphate solubility is observed to steadily increase with the replacement of larger for smaller alkaline earths in borosilicate glasses. Sulphate solubility in aluminosilicate glasses is not achieved as no sulphate can be retained in these compositions. Chloride solubility also increases from MgO-containing to BaO-containing borosilicate glasses like sulphate solubility. However, the retention of chloride in aluminosilicate glasses is selective and sensitive to compositions; barium aluminosilicate glass possesses the highest chloride solubility with the highest chloride retention. In contrast, molybdate solubility increases from BaO-containing to MgO-containing aluminosilicate glasses and from BaO-containing to CaO-containing borosilicate glasses. Molybdate is poorly soluble in magnesium borosilicate glass. Comparison of the behaviour of these three anionic species in glass suggests that the controlling factors for molybdate solubility may be very different from the other two. Finally three compositional parameters normalised cation field strength (NCFS), electronegativity index (XR) and cationic size (SR), which are related to cationic charge and size, but which differ from each other with respect to the contributions of each aspect, are used to express the solubility dependence of each species. Within narrow compositional variations in this study (equimolar substitution among alkaline earths) the above parameters seems to be quite applicable. But the compositional variations in literature glasses are much more complicated and the fittings may not apply. When combined with literature data, the best fitting for sulphate solubility is found with SR, the index of cationic size, with an increasing exponential relationship between solubility and SR. For chloride solubility with best fit is obtained with NCFS, the index of cation field strength, with a decreasing exponential relationship between solubility and NCFS. Nevertheless, no convincing correlation for molybdate has been achieved, although XR, the index of electronegativity of network modifiers, does show a general trend of increasing solubility with linearly decreasing XR.