The invention relates to a whey protein hydrolysate, in particular a hydrolysate consisting of whey protein enriched with α-lactalbumin and α-lactalbumin, and the use thereof for producing pharmaceuticals, anti-hypertensive agents, food supplements, foodstuffs and animal feed, and to pharmaceuticals, anti-hypertensive agents, food supplements, foodstuffs and animal feed produced in this manner. The whey protein hydrolysate according to the invention, which has an ACE inhibiting and anti-hypertensive action, contains a physiologically active quantity of at least one peptide containing tryptophan, preferably at least one of the bio-active dipeptides Ile-Trp and Trp-Leu, and can be obtained by the extensive hydrolysis of whey protein isolates or of pure α-lactalbumin.