A curable composition includesa first component containing aldehyde group-containing compounds which include at least one compound with two or more aldehyde groups anda second component containing 1,3 keto ester group-containing compounds which include at least one compound with two or more 1,3 keto ester groups of the formula (I), wherein the average molecular weight M.sub.n of at least one of the two components, with respect to the aldehyde or 1,3 keto ester group-containing compounds, ranges from 400 to 20,000 g/mol. The composition is largely free of toxic ingredients and cures in ambient conditions using conventional catalysts quickly in order to form a non-tacky elastic polymer with a high degree of strength and elasticity. The composition is particularly suitable for use as an elastic adhesive, sealant, or coating with a high degree of robustness during production, storage, and processing as well as a high degree of resistance after curing.