1,4-Diazabicyclo[2.2.2]octane and C-substituted 1,4-diazabicyclo[2.2.2]octanes of the formula (I) ##STR1## where R.sup.1 and R.sup.2 are each hydrogen or alkyl or alkenyl, each of 1 to 4 carbon atoms, are prepared from a heterocyclic amine of the formula (II) ##STR2## where R.sup.1 and R.sup.2 have the above meanings, R.sup.3 is hydrogen, hydroxyethyl or aminoethyl and X is hydroxyl or amino, in the presence of borosilicate and/or iron silicate zeolites as catalysts. Particularly suitable catalysts are the borosilicate and iron silicate zeolites of the pentasil type.