The invention relates to a composition comprising at least one XAP peptide, in which X is the empty set or a valine, for use thereof in preventing and/or treating pathological conditions associated with alpha-glucosidase. The invention also relates to the use of a hydrolysate of at least one protein, said protein comprising or consisting of at least 0.05% to <;5% or of at least 5% of XAP units, in which X is the empty set or a valine, for use thereof in preventing and/or treating pathological conditions associated with alpha-glucosidase.