The present invention relates to piperidines denoted by the formula: ##STR1## in which X is the 4-fluorobenzoyl, 2-(4-fluorophenyl)-1,3-dioxolan-2-yl or 6-fluoro-1,2-benzisoxazol-3-yl group, Y is a hydrogen atom or the hydroxyl group, m is an integer between 0 and 4 inclusive, n is 0 or 1, Q is a nitrogen atom or the methine group; when Q is a nitrogen atom, R is the cyano group or the carbamoyl group; when Q is the methine group, R is the nitro group; R.sup.1 and R.sup.2 may be identical or different and are hydrogen, a lower alkyl radical, the phenyl radical, the 2,2,2-trifluoroethyl group or the 2-[4-(4-fluorobenzoyl)-1-piperidinyl]ethyl group; or the NR.sup.1 R.sup.2 structural unit is the piperidino radical or the 4-(4-fluorobenzoyl)-1-piperidinyl group.Application of these compounds as antihypertensive medications.