A polymer composition usable for the production of articles of biodegradable plastics material includes an ethylene/vinyl alcohol copolymer and destructured starch. Preferably, the composition is obtainable by mixing the ethylene/vinyl alcohol copolymer, in a heated extruder, with a starch component constituted by a destructured starch composition produced beforehand by mixing starch with a high-boiling plasticizer, such as glycerine and a destructuring agent, preferably constituted by urea, in an extruder. Alternatively, the composition can be obtained by mixing the ethylene/vinyl alcohol copolymer with starch and a plasticizer in an extruder, with water added as appropriate and possibly with a suitable destructuring agent.; The composition is particularly useful for the production of films with good resistance to perforation and tearing and moulded articles with improved mechanical strength. The products made from this composition are also good oxygen and carbon dioxide barriers.