A nonlinear model of unemployment is formulated and applied in this paper. The formulation is motivated by a Keynesian principle of weak aggregate demand. The basic idea is that the rise of unemployment causes the fall of aggregate demand for final goods. This in turn leads to the fall of the demand for labor, which leads to even higher unemployment. The model is econometrically estimated for the Eurozone and it is shown that the described mechanism gives rise to the multiplicity of the equilibrium rate of unemployment. Factors influencing the position of the equilibrium points are studied and economic implications are made from this analysis.