We report the investigation of rubbery double networks that are based on poly(n-butyl acrylate) (BA) backbones and feature either non-covalent or covalent cross-links. The polymers for the supramolecular network were prepared by reversible addition−fragmentation chain-transfer polymerization of n-butyl acrylate and up to 10 mol% of the self-complementary hydrogen bonding motif 2-ureido-4[1H]pyrimidinone (UPy), which dimerizes into supramolecular cross-links. The covalent polymer network was synthesized by UV-initiated free-radical polymerization of BA and up to 5 mol% of the difunctional cross-linker 1,4-butanediol diacrylate, either separately, or after imbibing films of the supramolecular network with the reaction mixture for the covalent network. The combination of the two network types affords materials that show features of both single networks. The co-existence of a static and a dynamic network affords materials that owe their high thermal stability and creep resistance to the covalent network, and their high extensibility and healability to the supramolecular network.