A process for the manufacture of a nitrogen-containing crystalline metal silicate having a zeolite structure from silicon dioxide and a metal oxide and/or metal hydroxide, wherein the crystallization is carried out in the absence of an alkali metal in an aqueous solution of hexamethylenediamine, preferably under the autogeneous pressure of the solution at from 100.degree. to 200.degree. C. The zeolites are preferably used as catalysts for the reaction of methanol and/or dimethyl ether to give unsaturated hydrocarbons, the oligomerization of olefins, the alkylation of aromatics, and other conversions of hydrocarbons.