Two player zero sum differential games are an extension of optimal control problems. When the cost or payoff is the integral of some function h up to the first time the trajectory enters a “terminal set” the differential game is one of survival. If $h \equiv 1$, the payoff is just the time elapsed up to the “capture time” and the game is one of pursuit and evasion. If $h \geqq 1$, the game is called a generalized pursuit-evasion game, and in previous papers it has been shown- that when the Isaacs condition is satisfied the upper and lower “extended” values of such a differential game are equal—that is, the game “has extended value”. In the present note this result is proved under the weaker condition that $\max _y \min _z h(t,x,y,z) \geqq 0$.