This paper analyzes some important factors determining firms' innovative activity by using a dynamic stochastic oligopoly model. We suppose that the rivals in an industry maximize their expected discounted cash flows with respect to R&D expenditures and output levels. Optimal innovative activity is shown to depend positively on market size, but negatively on demand and technological uncertainty, spillovers, and interest rates. Using an isoelastic demand function, we can show that, if spillovers are modest and demand is relatively inelastic, firms' maximum innovative activity is not necessarily to be expected in the monopoly case. The maximum may also occur in either a duopoly or triopoly.