Characterizations of open-loop Stackelberg strategy for two-person nonzero-sum dynamic games described by linear operators (including unbounded ones) in Hilbert spaces are presented. The method of Lions is used and it guarantees the existence, uniqueness, as well as necessary and sufficient conditions for the open-loop Stackelberg strategy of such games. Special cases considered include games governed by ordinary differential equations, linear elliptic and parabolic partial differential equations with quadratic cost functions.