New crosslinked 1,2,4-oxadiazole elastomers were prepared by thermally condensing a monomer having the formula H2N(HON)C-R-Q, wherein Q is a triazine ring-forming group such as nitrile or amidine or a mixture of such group with amidoxime, or a mixture of said monomer with R C(NOH)NH2 sub 2 with R in these formulas standing for a bivalent organic radical. In the monomer charge, the overall proportions of amidoxime groups to triazine ring-forming groups varies depending on the extent of crosslinking desired in the final polymer