We theoretically analyse the relationship between corporate social responsibility (CSR) and tax avoidance of an oligopolistic firm. The firm maximizes a weighted sum of profits and a CSR objective that depends on output and the firm's contribution to public good provision, that is, tax payments. Making one CSR element more important induces the firm to adhere less to the other and to reduce tax avoidance. Hence, simultaneously a substitutive and a complementary relationship between CSR and tax avoidance can be observed. Therefore, using composite indicators of CSR prevents an empirical identification of this linkage. Moreover, if tax avoidance declines, CSR activities will increase. Consequently, the overall link between CSR and tax avoidance is theoretically ambiguous.