The present invention relates to the use of N-acylvanillinamide derivatives capable of activating the peripheral receptor CB1 of cannabinoids. In particular, the present invention relates to the use of compounds of general formula (I) ##STR00001## in which the meanings of R, R.sub.1, R.sub.3 and Y are as defined in the description, for the preparation of a medicinal product which is capable of activating the peripheral receptor CB1 of cannabinoids.