The invention relates to the use in the preparation of medicines having activity of the antihypertensive type, useful for treating or preventing hypertension, of one or more peptides having inhibiting activity on ACE with IC.sub.50 values of the order of or less than 60 .mu.M, selected from the group of peptides having the following amino acid sequences: TABLE-US-00001 Thr-Val-Tyr (SEQ ID No.: 1) Asn-Met-Ala-Ile-Asn-Pro-Ser-Lys (SEQ ID No.: 2) Phe-Ala-Leu-Pro-Gln-Tyr (SEQ ID No.: 3) Phe-Pro-Gln-Tyr-Leu-Gln-Tyr (SEQ ID No.: 4) Phe-Ala-Leu-Pro-Gln-Tyr-Leu-Lys (SEQ ID No.: 5) Asn-Met-Ala-Ile-Asn-Pro (SEQ ID No.: 6) Phe-Ala-Leu-Pro. (SEQ ID No.: 7) The invention also relates to a pharmaceutical composition containing as its active principle an effective quantity of one or more of the above-cited peptides in combination with a pharmaceutically acceptable vehicle. The invention also relates to a food product, in particular suitable for supplementing the diet of people subject to hypertension or seeking to prevent the appearance thereof, containing an effective quantity of one or more of the above-cited peptides, in combination with food supports, in particular proteins, lipids, or carbohydrates. Such a food product may also include at least one of the peptides having the following amino acid sequences: TABLE-US-00002 Ala-Leu-Asn-Glu-Ile-Asn-Gln-Phe- (SEQ ID No.: 8) Tyr-Gln-Lys Ala-Leu-Asn-Glu-Ile-Asn-Gln-Phe- (SEQ ID No.: 9) Tyr Tyr-Leu. (SEQ ID No.: 10)