This paper is devoted to a new class of differential games with continuous updating. It is assumed that at each time instant, players have or use information about the game defined on a closed time interval. However, as the time evolves, information about the game updates, namely, there is a continuous shift of time interval, which determines the information available to players. Information about the game is the information about motion equations and payoff functions of players. For this class of games, the direct application of classical approaches to the determination of optimality principles such as Nash equilibrium is not possible. The subject of the current paper is the construction of solution concept similar to Nash equilibrium for this class of differential games and corresponding optimality conditions, in particular, modernized Hamilton-Jacobi-Bellman equations.