This paper considers a one-stage Cournot duopoly of R&D. We characterize the Nash equilibrium of the one-stage game and provide a comparison with the two-stage version of the same Cournot model of R&D/product market competition. We look at R&D expenditures, profits, output and welfare. Under perfect symmetry, the one-stage model always leads to higher profits when the spillover parameter is not equal to 1/2. Moreover, the one-stage model implies more R&D expenditure and higher welfare if and only if the spillover parameter is greater than 1/2. The insights are robust to an n-firm generalization, but the differences between the one-stage game and the two-stage game disappear as the market becomes perfectly competitive.