Extended Oligopoly models will be introduced and examined in which the firms might face capacity limits, thresholds for minimal and maximal moves, and antitrust thresholds in the case of partial cooperation. Similar situation occurs when there is an additional cost of output adjustment, which is discontinuous at zero due to set-up costs. In these cases the payoff functions of the firms are nondifferentiable and in some cases even discontinuous. Under the usual concavity assumptions Cournot oligopolies have monotonic response functions and unique Cournot-Nash equilibrium. However the introduction of these more realistic additions into the oligopoly models creates a fundamentally new situation: the existence of no equilibrium or the presence of multiple, in some cases even infinitely many, equilibria. It also results in a very different asymptotic behavior of the dynamic extensions. The paper gives a brief survey of the relevant models, derives the response functions of the firms, and examines the existence and the number of equilibria. In the case of infinitely many equilibria the equilibrium-set will be also determined and characterized.