Oligomers and polymers containing epoxide groups and silane groups and preparable by reacting (A) at least one low molecular mass, oligomeric or polymeric compound containing at least two epoxide groups (a1) with (B) at least one silane containing (b1) at least one at least divalent organic radical which per se is not hydrolyzable, (b2) at least one cyclic dicarboxylic anhydride group and (b3) at least one silane group containing at least one hydrolyzable group (b31), the cyclic dicarboxylic anhydride groups (b2) being attached to the silane groups (b3) via the radicals (b1), the equivalent ratio of epoxide groups (a1) to dicarboxylic anhydride groups (b2) being 0.7 to 100; processes for preparing them, and their use for preparing anhydrous curable compositions.