In this article, the stability of sols of detonated nanodiamonds, DND, with positively charged colloidal particles, is studied in different salt solutions in water–dimethyl sulfoxide (DMSO) binary systems containing 95 vol.% organic solvent. Additionally, several CCC values are determined in 95 vol.% acetonitrile for comparison. The critical coagulation concentrations (CCC) are determined using the dynamic light scattering technique and the Fuchs function. As coagulators, NaCl, NaBr, NaNO3, NaClO4, Nan-C8H17SO3, and Nan-C12H25OSO3 are used. Comparison of the CCC values in DMSO–H2O and CH3CN–H2O with those obtained in water allows us to make some conclusions. The variations of these values in different solvents are explained in terms of good and poor interfacial solvation of colloidal particles, “structural” contribution to the interparticle interaction energy, lyotropic series for anions, and more or less pronounced adsorption of surfactants. The study of the stability of DND hydrosol in solutions of anionic surfactants with different hydrocarbon tail length demonstrated the crucial role of adsorption in the coagulation process.