This study analyses whether or not the effect of board independence on a firm's strategic performance is moderated by family involvement in ownership and control. Moderation of the board's size and the independent director ratio are tested under quadratic specifications. The effect of CEO duality with family involvement on long-term sales growth is also measured. The empirical analysis is conducted in the Southern European context using a sample of publicly traded firms that have concentrated ownership structures. The main findings indicate that when nonlinearities are considered, family involvement moderates the relationship between the independent director ratio and firm performance. The optimal proportion of independent directors is lower in family businesses than in non-family ones. However, the results fail to support nonlinearities for board size. We find positive linear relationships between both board size and CEO duality with firm performance, which are not moderated by family involvement.