A constant stream of identical cash flows with no end.  The formula for determining the present value of a perpetuity is as follows:   

|||This is not as abstract a concept as you may think; the British issued bonds, called consols, which are a great example of a perpetuity. By purchasing a consol from the British government, the bondholder is entitled to receive annual interest payments forever. Although it may seem a bit illogical, an infinite series of cash flows can have a finite present value. Because of the time value of money, each payment is only a fraction of the last.  The concept of a perpetuity is used often in financial theory, such as the dividend discount model (DDM).