Process for the preparation of N-vinylcarboxamides by pyrolysis of a compound of the formula CH3—CH(CN)—N(R)—CO—R1  (I), in which R and R1 are H or C1- to C6-alkyl, in the presence of solids which are doped with alkali metal or alkaline earth metal ions, under reduced pressure at a temperature of from 330 to 750° C. with elimination of hydrogen cyanide, cooling, separation and isolation of the reaction products, a solid arranged in a tubular reactor being treated at a temperature in the range from 0 to 250° C. with a solution of an alkali metal and/or alkaline earth metal base, the solution being discharged, the remaining solvent which adheres to the catalyst thus obtainable being evaporated and said catalyst then being heated to a temperature of at least 380° C. for activation.