This paper examines the impact of voluntary export restraints (VERs) in an international duopoly modelled as a differential game. We employ two well known capital accumulation dynamics for firms, due to Herlove and Arrow and to Ramsey, respectively. First we investigate Cournot behavour, showing that, in both models, a VERs cannot ne "voluntarily" employedby the foreign firms. Our analysis therefore suggests that the empirical observation of VERs corresponds to their use either as coordinating or as quasi-collusive devices in markets where firms are price setters and sales are not capacity-constrained. This is confirmed by our analysis of price competition. The Bertrand steady state of the Solow-Nerlove-Arrow model coincides with the Cournot equilibrium, and therefore the foreign firm cannot be expected to voluntarily adopt an export restraint. However, the opposite holds in the case of price behavior in the ramsey setting, where the adoption of anexport restraint may increase the profits of both firms.