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In this paper, the transient stability and voltage regulation of multimachine power systems are simultaneously addressed in a multivariable and nonlinear framework. Power systems are nonlinear, large-scale and made of highly coupled generators having a wide range of operating points. Decentralized nonlinear adaptive controllers which continuously update their parameters to compensate for changes in operating points are proposed. The design method is based on a new power system model recently introduced by the authors. The main characteristic of the new model is that interactions between generators and changes in operating conditions are represented by time-varying parameters. The parameters have fixed parts, which depend on the steady-state active and reactive power delivered by each generator, and time-varying parts modelling the interactions between generators, which are treated as disturbances. More importantly, the new model permits the formulation of a control design scheme, which consists of applying the input-output linearization method and stabilizing the resulting partially linear system by a linear control law. The fixed linear gains are computed from an algebraic Riccati equation and considerably attenuate the disturbance effects. An adaptive law derived from the Lyapunov stability method ensures that the controller parameters are bounded and that the generator signals converge asymptotically to steady-state values. The robustness of the controller is used to compensate for the disturbances, while its adaptive nature is used to compensate for load variations that induce operating-point variations. A four-machine power system is used to assess the effectiveness of the multivariable regulator. Simulation results show that good performance in closed loop is achieved.