In standard models of the labor market, supply slopes upwards and demand slopes downwards in a real wage employment space. Supply and demand schedules mostly intersect at rather steep slopes to assure stability, although the empirical evidence on labor supply and labor demand elasticities in equilibrium cannot be pinpointed to single values. Knowing that narrow bandwidths for labor supply and demand elasticities do not exist, there is surprisingly little concern about what would happen in these models from a dynamic perspective if labor demand and supply intersect at flat angles. What are the features of a labor market where the supply of labor and the demand for labor are very elastic? If a real wage increase induces a comparably large increase in the supply of labor, and by the same time a large decrease in the demand for labor, a deviation from equilibrium might destabilize the market or lead to very long adjustment paths. After a negative productivity shock, for example, it might take a very long time until real wages and employment reach the new equilibrium. If the shift of the demand curve yields a new equilibrium where supply and demand intersect at even flatter angles, the equilibrium might become unstable. Maybe it is the more likely unstable equilibrium that lead to a minor interest in labor markets that have flat supply and demand curves, since when these curves are linear, the labor market would become globally unstable. Of course, an explosive system is not a desirable outcome. It can hardly explain anything. Nonlinear supply and demand curves bring in some new aspects. A labor market equilibrium with flat supply and demand curves may only be locally unstable. Furthermore, nonmonotonous supply and demand curves can intersect at more than one employment level or may not intersect at all. Such labor market models open the door to ‘fragile equilibria’ (Blanchard and Summers 1988) that may cope well with some of the stylized facts on European unemployment. Besides long adjustment periods and locally unstable equilibria, dynamics can become irregular. Real wages may never find their way to the labor market equilibrium. Time series would appear to be random, even though the underlying labor market model is deterministic. Real wage and employment dynamics would be endogenous and cycles self-sustained.