The invention relates to the production of bioactive products that are derived from milk proteins for the production of bioactive milk products derived from milk proteins, particularly caseins. The 16 inventive peptides can be obtained chemically, biotechnologically or by means of enzymatic treatment from proteins containing same and give rise to peptides with an antimicrobial activity, an in vitro angiotensin converter inhibitor activity and/or antihypertensive activity and/or antioxidant activity. Said nutraceutical products are suitable for use in the food and pharmaceutical industries, both in the form of a hydrolyzate or bioactive peptides.