A process for preparing amine oxides of the general formula I ##STR1## where R.sup.1, R.sup.2 and R.sup.3 are each C.sub.1 -C.sub.30 -alkyl, C.sub.3 -C.sub.12 -cycloalkyl, C.sub.1 -C.sub.30 -hydroxyalkyl, C.sub.1 -C.sub.30 -aminoalkyl, C.sub.2 -C.sub.30 -alkoxyalkyl, aryl, C.sub.7 -C.sub.20 -aralkyl, C.sub.7 -C.sub.20 -alkylaryl, C.sub.1 -C.sub.8 -alkyl-, C.sub.1 -C.sub.8 -alkoxy- or halogen-monosubstituted, -disubstituted, -trisubstituted, -tetrasubstituted or -pentasubstituted C.sub.3 -C.sub.12 -cycloalkyl, aryl, C.sub.7 -C.sub.20 -aralkyl, C.sub.7 -C.sub.20 -alkylaryl, --[(CH.sub.2).sub.2 --O].sub.n --R.sup.4, --{[CH(CH.sub.3)CH.sub.2 ]--O}.sub.m --R.sup.5, or R.sup.1 and R.sup.2 are together an uninterrupted or oxygen-, nitrogen- or sulfur-interrupted C.sub.3 -C.sub.12 -alkylene diradical chainR.sup.4 and R.sup.5 are each C.sub.1 -C.sub.12 -alkyl, C.sub.3 -C.sub.12 -cycloalkyl, hydroxyl, --COR.sup.6 or --CH.sub.2 --COOR.sup.7, C.sub.3 -C.sub.12 -cycloalkyl, aryl, C.sub.7 -C.sub.20 -aralkyl or C.sub.7 -C.sub.20 -alkylaryl,R.sup.6 and R.sup.7 are each C.sub.1 -C.sub.12 -alkyl or C.sub.3 -C.sub.12 -cycloalkyl, andm and n are each from 1 to 40,from amines of the general formula II ##STR2## where R.sup.1, R.sup.2 and R.sup.3 are each as defined above, using hydrogen/oxygen mixtures at temperatures from (-5.degree.) to 90.degree. C. and pressures from 1 to 100 bar in the presence of oxidation catalysts comprises using as oxidation catalysts those of group VIII of the periodic table on titanium silicates, vanadium silicates or their mixtures with a zeolite structure.