This study examines whether health care is affected by Baumol's cost disease in a scenario of no growth. Baumol's model implies that stagnant sectors are driven by wage increases in excess of productivity growth. But in a no growth economy the income is constant. It is investigated in two institutional proposals, selective reduction of productivity and reduction of working hours. In both scenarios the cost disease does not affects the health care. However, in the second scenario an important result is found. In this sector, with slow productivity growth, will be necessary a greater number of workers. The relative cost of health care will increase over the years. Therefore, although the cost disease does not affect the health sector in a no growth economy, the relative cost of health should continue to rise.