Differential games of generalized pursuit and evasion are studied. The definitions of strategy and payoff follow those of Berkovitz. It is shown under appropriate hypotheses on the data of the problem that if the Isaacs condition holds, then there exists a saddle point. Then differential games with information lags are studied, in which Berkovitz’s definitions of strategy and payoff are generalized to games with lags. It is first shown through an example that if a game has a lag, then value of the game does not exist in general. For games of fixed duration with information lags, it is demonstrated that if the Isaacs condition holds, then as the lags tend to zero, the upper and lower values as functions of the lags will tend to the value in the game with no lags. The same results hold also for differential games of generalized pursuit and evasion and for games of survival if certain reasonable conditions on the data and the structure of the terminal set hold.