This paper investigates the constrained noncooperative games (NGs) of multi-agent systems. In contrast to existing NGs, our formulation involves the general linear dynamics of players, and the players are subject to both local and coupling nonlinear constraints. Owing to the general linear dynamics and the nonlinear constraints, existing generalized Nash equilibrium (GNE) seeking strategies are not applicable to our problem. Also, the general linear dynamics and the nonlinear constraints put obstacles in the way of strategy design and analysis, since the decisions cannot be determined by the control inputs of players directly, while the GNE must belong to the constraints. To seek the variational GNE (v-GNE) of the constrained NGs, two adaptive strategies are developed based on gradient descent, state/output feedback, and primal-dual methods. Compared with existing distributed strategies for NGs with physical systems, the two strategies are independent of global parameters or variables, which indicates the full distributivity of the two strategies. Furthermore, the two strategies are rigorously analyzed by virtue of variational analysis and LaSalle invariance principle. Under the two strategies, the general linear players globally converge to the exact v-GNE. Finally, the proposed methods are applied to the autonomous electricity market games (EMGs) of doubly-fed induction generators (DFIGs).