In this paper we study the paths of market prices and the extracted quantities of an exhaustible resource when the market ownership of the mines is of imperfect competition. The major part of the study is devoted to the Cournot—Nash case, with minor extensions to a Stackelberg duopoly and a cooperation between the two firms. The unique characteristics of the study is of perfect common property of the resource and perfect substitution of the rate of extraction and cummulative extraction in the costs of mining of each of the firms. If corner solutions are not a priori encountered, then the typical static characteristics are maintained also in the dynamic case.