1-Acylpiperidine compound of the formula I ##STR1## in which R.sub.1 is an optionally substituted aralkyl, aryloxyalkyl, heteroaralkyl, aroyl, heteroaroyl, cycloalkylcarbonyl, aralkanoyl, heteroarylalkanoyl, aralkoxycarbonyl or arylcarbamoyl radical or the acyl radical of an .alpha.-amino acid which is optionally N-substituted by lower alkanoyl or carbamoyl-lower-alkanoyl, R.sub.2 is cycloalkyl or an optionally substituted aryl or heteroaryl radical, R.sub.3 is hydrogen, alkyl, carbamoyl or an alkanoyl or alkenoyl radical which is optionally substituted by carboxyl or esterified or amidated carboxyl, R.sub.4 is an optionally substituted aryl or optionally partially hydrogenated heteroaryl radical, X.sub.1 is methylene, ethylene, a direct linkage, an optionally ketalised carbonyl group or an optionally etherified hydroxymethylene group, X.sub.2 is alkylene, carbonyl or a direct linkage, and X.sub.3 is carbonyl, oxo-lower-alkylene, oxo(aza)-lower-alkylene or an alkylene radical which is optionally substituted by phenyl, hydroxymethyl, optionally esterified or amidated carboxyl or, in higher than the .alpha. position, by hydroxyl, and its salts have substance-P-antagonistic properties and can be used as pharmaceutically active substances in pharmaceuticals for the treatment of disorders in whose development substance P plays an essential part.