The invention relates to new peptides formed of at least seven subsequent amino acids of the amino acids in position 12-40, counted from the N-terminal end, in the sequence constituting human lactoferrin, and preferably modifications thereof. The invention also relates to medicinal products comprising such peptides, especially intended for treatment and prevention of infections, inflammations and tumours. Furthermore, the invention relates to food stuff, e.g. infant formula food, comprising the above mentioned peptides.