This paper examines the case where a small open economy owns a stock of exhaustible resources like Chromium, Copper etc. which are not consumed domestically but exported. The resource earnings are used to import consumption goods. We will discuss the optimal production of this resource, when the terms of trade (faced by the country) follows an exogenous given time path that is subject to some stochastic fluctuations. It will come about that uncertainty concerning future values of the terms of trade affects the extraction dynamics for the following reasons. First, if the functions involved in the first-order conditions are nonlinear, the expected future value of these functions differs from a world of certainty. Consequently uncertainty has an impact on the behaviour of resource-exporting- countries. Note that this change in behaviour cannot be captured with certaintyequivalence. Second, if the costs of extraction exceed the gain from the resource use for some time due to stochastic fluctuations, the country can keep the resource in the ground but maintain the option of future extraction when depletion will become profitable again. So uncertainty creates an incentive to slow down production.