Equations for the calculation of the Kirkwood-Buff integrals (KBI) for the components of a ternary system from thermodynamic data are presented and applied to a number of mixtures of non-electrolytes. The mixtures comprise substances which may develope strong mutual interactions due to eg. permanent dipoles and hydrogen bonds; they are: (I) water-propan-1-ol-N,N-dimethylformamide (DMF), (II) water-ethane-l,2-diol-acetonitrile, (III) water-ethane-1,2-diol-ethanol, (IV) ethanol-trichloromethane-1,4-dioxane; the system (V), water-propanol-urea, previously studied is also discussed. The observed KBIs have been correlated to interactions among functional groups and to the structure of the solvent components. Moreover, a preferential solvation coefficient of a given compound with respect to the other two is given a different definition to that of previous authors and calculated; its change with changing concentration of solvating components is examined. These quantities have proved to be useful indicators of the predominant types of interactions in various concentration regions. In systems I and V we compare the effect of the addition of either DMF or urea to the binary mixture, water-propanol, which is characterised by large positive values of the like (i-i) KBI. A markedly different behaviour is found: whereas urea causes a strong increase of the like KBIs, DMF has the opposite effect. Moreover, urea is mostly solvated by water over the whole water-propanol mole fraction range, whilst DMF presents a sharp change of preference at ca. x(W) = 0.8, being preferentially solvated by propanol in the water-rich region. The results from systems II and III, where the effect of the addition of either ethanol or acetonitrile to the mixture water-ethanediol is examined show, in particular, that the KBIs of ethanol and acetonitrile behave as if the mixture water-ethanediol were a single component. In system IV the observed KBI behaviour is related to the competition between hydrogen-bond and dipole-dipole type interactions.