A thermoplastic or elastomeric composition, is characterized in that: a) it exhibits a degree of biodegradability of less than 50%, preferably less than 30%, and b) it contains at least 0.5% and at most 99.95% by weight of an ester of a starchy material, which has a degree of ester substitution (DS) of between 1.6 and 3, and at least 0.05% by weight and at most 99.5% by weight of a polymer other than starch.