The paper investigates the role of progressive income taxation in the frame of the basic multiplier-accelerator model in continuous time. It is shown that, while the proportional taxation is, as common wisdom believes, always stabilizing, in the case of non-linear progressive taxation, an increase of the degree of progression is always destabilizing. Moreover it is shown that in the presence of tax collection lags, the progressive taxation can have a twofold role, either stabilizing or destabilizing. Our results have a theoretical as well as a practical aspect. Firstly, they shed new light on the dynamic role of various economic behaviours such as the thriftiness of the agents, public expenditure, the maximal income tax rate and finally the degree of progression of income taxation. Secondly they show a further, so far neglected, factor causing economic fluctuations, through the complex effect of a progressive as well as lagged income tax. Thirdly, they provide the policy maker with clear stabilization rules and the warning of possible complicated dynamic configurations (such as the "corridor" stability case).