The present invention pertains to compositions containing a polycondensate and optionally an oil component, wherein the polycondensate is derived from a dicarboxylic acid component, a diol component and an ethylenically unsaturated dicarboxylic acid component. The composition of the invention may be cross-linked to yield an adhesive composition. The composition of the invention and the adhesive composition of the invention may be used on substrates such as tapes and patches in the medical field.