This paper studies the interplay between public and private health care in a National Health Service. We consider a two-stage game, where at stage one a Health Authority sets the public sector wage and a subsidy to (or tax on) private provision. At stage two the physicians decide how much to work in the public and the private sector. We characterise di¤erent equilibria depending on whether physicians coordinate labour supply or not, the physicians' job preferences, and the cost e¢ciency of private relative to public provision. We …nd that private provision tends to crowd out the NHS if physicians are su¢ciently indi¤erent about where to work or the private sector is su¢ciently cost e¢cient. Competition between physicians triggers a shift from public provision towards private provision, and an increase in the total amount of health care provided. The endogenous nature of labour supply may have counter-intuitive e¤ects. For example, a cost reduction in the private sector is followed by a higher wage in the public sector.JEL Classi…cation: I11, I18, J42, L33