Novel pyrimidine N-oxide compounds and salts thereof, well suited for stimulating the growth of keratin fibers (e.g., the hair or the eyelashes) and/or limiting the loss thereof and/or increasing their density, have the formula (A): ##STR00001## in which n is an integer ranging from 2 to 12; R.sub.1 is a linear or branched, saturated or unsaturated alkyl radical, optionally substituted with a group --OR', --NR'R'' or --COOR', R.sub.1 having from 1 to 20 carbon atoms, or is NR'R''; R.sub.2 is hydrogen, --NR.sub.3R.sub.4, --OR.sub.3, or --SR.sub.3, wherein R.sub.3 and R.sub.4, which may be identical or different, are each a linear or branched, saturated or unsaturated alkyl radical, optionally substituted with a group --OR', --NR'R'' or --COOR', R.sub.2 having from 1 to 20 carbon atoms, with the proviso that R.sub.3 and R.sub.4 may form part of a saturated or unsaturated ring member of 4 to 7 atoms, optionally containing at least one hetero atom; and R' and R'', which may be identical or different, are each hydrogen or a saturated, linear or branched C.sub.1-C.sub.3 alkyl radical.