The invention relates to a medicament which comprises a peptide extract of avocado and which can also comprise a composition containing D-mannoheptulose and/or perseitol, such as a water-soluble extract of avocado sugars, and/or a peptide extract of lupine. The inventive medicament is intended for the treatment and/or prevention of illnesses that are linked to an alteration in innate and/or acquired immunity, through an increase in the production of anti-microbial peptides, preferably hBD-2, without inducing inflammatory reactions, irritations or intolerances.