A method for controlling animal pests, which comprises treating the pests, their environment or the plants, surfaces, materials or spaces to be kept free from them with an effective amount of a compound of the formula I, where the substituents and the index have the following meanings: X is NOCH.sub.3, CHOCH.sub.3, CHCH.sub.3, and CHCH.sub.2 CH.sub.3 ; R.sup.1 is hydrogen and C.sub.1 -C.sub.4 -alkyl; R.sup.2 is cyano, nitro, trifluoromethyl, halogen, C.sub.1 -C.sub.4 -alkyl and C.sub.1 -C.sub.4 -alkoxy; m is 0, 1 or 2, it being possible for the R.sup.2 radicals to be different if m is 2; R.sup.3 is hydrogen, cyano, nitro, hydroxyl, amino, halogen, C.sub.1 -C.sub.4 -alkyl, C.sub.1 -C.sub.4 -haloalkyl, C.sub.1 -C.sub.4 -alkoxy, C.sub.1 -C.sub.4 -haloalkoxy, C.sub.1 -C.sub.4 -alkylthio; C.sub.1 -C.sub.4 -alkylamino or di-C.sub.1 -C.sub.4 -alkylamino; R.sup.4 is hydrogen, cyano, nitro, hydroxyl, amino, halogen, C.sub.1 -C.sub.6 -alkyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.2 -C.sub.6 -alkenyloxy, C.sub.2 -C.sub.6 -alkenylthio, C.sub.2 -C.sub.6 -alkenylamino, N--C.sub.2 -C.sub.6 -alkenyl-N--C.sub.1 -C.sub.6 -alkylamino, C.sub.2 -C.sub.6 -alkynyl, C.sub.2 -C.sub.6 -alkynyloxy, C.sub.2 -C.sub.6 -alkynylthio, C.sub.2 -C.sub.6 -alkynylamino, N--C.sub.2 -C.sub.6 -alkynyl-N--C.sub.1 -C.sub.6 -alkylamino, it being possible for the hydrocarbon radicals of these groups to be partly or completely hydrogenated or to carry one to three of the following radicals: cyano, nitro, hydroxyl, mercapto, amino, carboxyl, aminocarbonyl, aminothiocarbonyl, halogen, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminocarbonyl, C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, C.sub.1 -C.sub.6 -alkylsulfonyl, C.sub.1 -C.sub.6 -alkylsulfoxyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -haloalkoxy, C.sub.1 -C.sub.6 -alkoxycarbonyl, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.2 -C.sub.6 -alkenyloxy, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.3 -C.sub.6 -cycloalkoxy, heterocyclyl, heterocyclyloxy, aryl, aryloxy, aryl-C.sub.1 -C.sub.4 -alkoxy, arylthio, aryl-C.sub.1 -C.sub.4 -alkylthio, hetaryl, hetaryloxy, hetaryl-C.sub.1 -C.sub.4 -alkoxy, hetarylthio, hetaryl-C.sub.1 -C.sub.4 -alkylthio, it being possible for the cyclic radicals in turn to be partly or completely halogenated and/or to carry one to three of the following groups: cyano, nitro, hydroxyl, mercapto, amino, carboxyl, aminocarbonyl, aminothiocarbonyl, C.sub.1 -C.sub.6 -alkyl, C.sub.1 -C.sub.6 -haloalkyl, C.sub.1 -C.sub.6 -alkylsulfonyl, C.sub.1 -C.sub.6 -alkylsulfoxyl, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -haloalkoxy, C.sub.1 -C.sub.6 -alkoxycarbonyl, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminocarbonyl, C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, di-C1.sub.-- C6-alkylaminothiocarbonyl, C.sub.2 -C.sub.6 -alkenyl, C.sub.2 -C.sub.6 -alkenyloxy, benzyl, benzyloxy, aryl, aryloxy, arylthio, hetaryl, hetaryloxy, hetarylthio and C(.dbd.NOR.sup.6)--A.sub.n --R.sup.7 ; C.sub.3 -C.sub.6 -cycloalkyl, C.sub.3 -C.sub.6 -cycloalkoxy, C.sub.3 -C.sub.6 -cycloalkylthio, C.sub.3 -C.sub.6 -cycloalkylamino, N--C.sub.3 -C.sub.6 -cycloalkyl-N--C.sub.1 -C.sub.6 -alkylamino, C.sub.3 -C.sub.6 -cycloalkenyl, C.sub.3 -C.sub.6 -cycloalkenyloxy, C.sub.3 -C.sub.6 -cycloalkenylthio, C.sub.3 -C.sub.6 -cycloalkenylamino, N--C.sub.3 -C.sub.6 -cycloalkenyl-N--C.sub.1 -C.sub.6 -alkylamino, heterocyclyl, heterocyclyloxy, heterocyclylthio, heterocyclylamino, N-heterocyclyl-N--C.sub.1 -C.sub.6 -alkylamino, aryl, aryloxy, arylthio, arylamino, N-aryl-N--C.sub.1 -C.sub.6 -alkylamino, hetaryl, hetaryloxy, hetarylthio, hetarylamino, N-hetaryl-N--C.sub.1 -C.sub.6 -alkylamino, it being possible for the cyclic radicals to be partly or completely halogenated or to carry one to three of the following groups: cyano, nitro, hydroxyl, mercapto, amino, carboxyl, aminocarbonyl, aminothiocarbonyl, halogen, C.sub.1 -C.sub.6 -alkyl, C.sub.1 -C.sub.6 -haloalkyl, C.sub.1 -C.sub.6 -alkylsulfonyl, C.sub.1 -C.sub.6 -alkylsulfoxyl, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -haloalkoxy, C.sub.1 -C.sub.6 -alkoxycarbonyl, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminocarbonyl, C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, C.sub.2 -C.sub.6 -alkenyl, C.sub.2 -C.sub.6 -alkenyloxy, benzyl, benzyloxy, aryl, aryloxy, hetaryl and hetaryloxy; R.sup.5 is hydrogen, C.sub.1 -C.sub.10 -alkyl, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.2 -C.sub.10 -alkenyl, C.sub.2 -C.sub.10 -alkynyl, C.sub.1 -C.sub.10 -alkylcarbonyl, C.sub.2 -C.sub.10 -alkenylcarbonyl, C.sub.3 -C.sub.10 -alkynylcarbonyl or C.sub.1 -C.sub.10 -alkylsulfonyl, it being possible for these radicals to be partly or completely halogenated or to carry one to three of the following groups: cyano, nitro, hydroxyl, mercapto, amino, carboxyl, aminocarbonyl, aminothiocarbonyl, halogen, C.sub.1 -C.sub.6 -alkyl, C.sub.1 -C.sub.6 -haloalkyl, C.sub.1 -C.sub.6 -alkylsulfonyl, C.sub.1 -C.sub.6 -alkylsulfoxyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -haloalkoxy, C.sub.1 -C.sub.6 -alkoxycarbonyl, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminocarbonyl, C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, C.sub.2 -C.sub.6 -alkenyl, C.sub.2 -C.sub.6 -alkenyloxy, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.3 -C.sub.6 -cycloalkoxy, heterocyclyl, heterocyclyloxy, benzyl, benzyloxy, aryl, aryloxy, arylthio, hetaryl, hetaryloxy and hetarylthio, it being possible for the cyclic groups in turn to be partly or completely halogenated or to carry one to three of the following groups: cyano, nitro, hydroxyl, mercapto, amino, carboxyl, aminocarbonyl, aminothiocarbonyl, halogen, C.sub.1 -C.sub.6 -alkyl, C.sub.1 -C.sub.6 -haloalkyl, C.sub.1 -C.sub.6 -alkylsulfonyl, C.sub.1 -C.sub.6 -alkylsulfoxyl, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -haloalkoxy, C.sub.1 -C.sub.6 -alkoxycarbonyl, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminocarbonyl, C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, C.sub.2 -C.sub.6 -alkenyl, C.sub.2 -C.sub.6 -alkenyloxy, benzyl, benzyloxy, aryl, aryloxy, arylthio, hetaryl, hetaryloxy, hetarylthio or C(.dbd.NOR.sup.6)--A.sub.n --R.sup.7 ; aryl, arylcarbonyl, arylsulfonyl, hetaryl, hetarylcarbonyl or hetarylsulfonyl, it being possible for these radicals to be partly or completely halogenated or to carry one to three of the following groups: cyano, nitro, hydroxyl, mercapto, amino, carboxyl, aminocarbonyl, aminothiocarbonyl, halogen, C.sub.1 -C.sub.6 -alkyl, C.sub.1 -C.sub.6 -haloalkyl, C.sub.1 -C.sub.6 -alkylcarbonyl, C.sub.1 -C.sub.6 -alkylsulfonyl, C.sub.1 -C.sub.6 -alkylsulfoxyl, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.1 -C.sub.6 -alkoxy, C.sub.1 -C.sub.6 -haloalkoxy, C.sub.1 -C.sub.6 -alkoxycarbonyl, C.sub.1 -C.sub.6 -alkylthio, C.sub.1 -C.sub.6 -alkylamino, di-C.sub.1 -C.sub.6 -alkylamino, C.sub.1 -C.sub.6 -alkylaminocarbonyl, di-C.sub.1 -C.sub.6 -alkylaminocarbonyl, C.sub.1 -C.sub.6 -alkylaminothiocarbonyl, C2.sub.2 -C.sub.6 -alkenyloxy, benzyl, benzyloxy, aryl, aryloxy, hetaryl, hetaryloxy or C(.dbd.NOR.sup.6)--A.sub.n --R.sup.7 ; where A is oxygen, sulfur or nitrogen and where the nitrogen carries hydrogen or C.sub.1 -C.sub.6 -alkyl; n is 0 or 1; R.sup.6 is hydrogen or C.sub.1 -C.sub.6 -alkyl and R.sup.7 is hydrogen or C.sub.1 -C.sub.6 -alkyl, wherein heterocyclyl is a member selected from the group consisting of three- to six-membered, saturated or partly unsaturated mono- or polycyclic heterocycles, which contain one to three heteroatoms selected from a group consisting of oxygen, nitrogen and sulfur; aryl is a member selected from the group consisting of aromatic mono- or polycyclic hydrocarbon radicals; and hetaryl is a member selected from the group consisting of aromatic mono- or polycyclic radicals which, in addition to carbon ring members, contain one to four nitrogen atoms or one to three nitrogen atoms and an oxygen or a sulfur atom or an oxygen or a sulfur atom, and its salts.