This paper contributes to the growing evidence that Irish and foreign‐owned firms based in Ireland conduct their innovation activities differently from each other. It tests the Cohen and Levinthal hypothesis, separately for Irish and foreign‐owned firms, that undertaking R&D and collaborating with external networks together enhance the probability of product and process innovation. To control for potential endogeneity of the external networking variables, a two‐step procedure is used with predicted probabilities used as instruments in the estimated production functions. Based on data from the Irish Community Innovation Survey 2006 to 2008, the results suggest that Irish‐owned firms which engage in external networks with public knowledge sources, while simultaneously undertaking R&D, are more likely to innovate than firms which perform these two activities individually. Irish‐owned firms which engage in backward networking for product and forward networking for process innovation while also undertaking R&D are less likely to be innovative, perhaps suggesting a substitution effect. These results for Irish‐owned firms provide some support for Cohen and Levinthal's hypothesis. However, foreign‐owned firms seem to behave differently, being largely self‐contained and relying exclusively on intramural R&D for innovation as the external networking variables, both individually and when interacted with R&D, have no effect on innovation likelihood.