To survive, an informational macromolecule must solve the major problem set by its very polymeric nature: instability. This is especially true in prebiotic terms because of the presumed initial absence of protective structures (proteins, lipids, etc.). We have analyzed the stability of the beta-glycosidic and of the 3'- and 5'-phosphoester bonds in both deoxy monomers and deoxy oligomers under a large set of conditions. The results show a strong dependence of the relative stability of these bonds on the physico-chemical environment. A set of conditions has been identified in which the stability of polymers becomes comparable with that of the precursor monomers. In certain instances the stability of the 5'-phosphoester bond is even higher in the polymer than in the mononucleotide.