International audienceThis paper explores the relationship between corporate social responsibility (CSR) and innovation from a firm strategic perspective. Matching Community Innovation Survey data with specific data collected about the CSR behaviour of Luxembourg firms, the authors identify two types of firms (strategic versus responsive) that differ in the intensity of their CSR adoption. A bivariate probit model, estimated to explain the different types of technological innovations (product and/or process), shows that firms with strategic CSR profiles are more likely to innovate in both products and processes. In contrast, adopting responsive CSR practices significantly alters firms' innovation, such that CSR may create barriers to innovation. These results have implications for theory and offer managerial recommendations for firms designing their innovation strategies