T HE object of this paper is to demonstrate that it is exceedingly difficult, if not impossible, to develop a theory of the business cycle on the basis of a simple multiplier-accelerator model. Such theories have experienced considerable popularity during the postwar years, even though it can be shown that they do not constitute internally consistent systems useful in describing the economic instability encountered in capitalistic economies. The particular cycle models under discussion here assume a relatively high capital-output coefficient which implies an excessive degree of income instability. To avoid unrealistically high or low levels of income, exogenous ceilings and floors are introduced into the model which limit income changes in either direction. Here it will be demonstrated that the subsidiary assumption of floors and ceilings represents a curiously round-about method of avoiding most implications of the assumption of the fixed capital-output ratio which underlies the whole model. It is necessary to substitute a more flexible production function for the postulated constant accelerator in order to avoid these unrealistic implications within a fairly simple theoretical model. The nonlinear accelerator model, which was developed by Hicks and Goodwin, is probably the most sophisticated model built upon the interaction of constant multiplier and acceleration coefficients.' Here we shall use the Hicks model as an example. Already in his review of Harrod's Towards a Dynamic Economics, Hicks presented an outline of his later theory and stated what he conceived to be the central problem of a theory of economic instability: