A process for preparing unsaturated nitriles of the formula I ##STR1## where R, R.sup.1 and R.sup.2 are each independently of one another alkyl or alkenyl each having 1-20 carbon atoms or cycloalkyl or cycloalkenyl each having 3-12 carbon atoms and any two of the radicals R, R.sup.1 and R.sup.2 may be part of a saturated or unsaturated ring and R.sup.1 and R.sup.2 may also be hydrogen and n is 0 or 1-20, by dehydration of oximes of the formula II ##STR2## where R, R.sup.1, R.sup.2 and n are as defined above, comprises dehydrating in the gas or liquid phase at from 150.degree. to 300.degree. C. over a heterogeneous catalyst consisting of an oxidic, carbidic or nitridic support doped with basic oxides and/or hydroxides or compounds which are converted into said oxides or hydroxides under the reaction conditions, or of said basic oxides.