Experimental basaltic glass dissolution in fresh water is compared with analyses made on subglacial hyaloclastites from Iceland. The dissolution is initially selective and remains selective if the solution is renewed, whereas it becomes apparently congruent in non-renewed conditions. The congruent dissolution is ascribed to a pH increase (up to 7.0–7.5) which is hampered in the former conditions. The palagonite hydrated layer on the Icelandic basaltic glasses is made up of amorphous to crystallized clay-like materials. The chemical composition of palagonite is close to that of the intergranular clayey material, thus, it is inferred that in most cases no significant chemical gradient exists in the solution between the reaction zone, namely the glass/palagonite interface, and the intergranular solution. We conclude that the dissolution of basaltic glass under subglacial conditions is controlled by thermodynamics and that kinetic constraints, such as the diffusion of species through the altered layers, do not play a major role.