Based on an adaptive backstepping approach, this study proposes a new coordinated control design where the coordination is done between the excitation controller of synchronous generators and steam-valve controller of turbine-governor systems in a multimachine power system by considering the critical parameters of both systems as unknown. This new coordinated control scheme can ensure the stability of multimachine power systems through the formulation of control Lyapunov functions (CLFs) and derive the adaptation laws to estimate the unknown parameters in the design process to prove the convergence of power systems using CLFs. The performances of the proposed control scheme are evaluated on a two-area four-machine 11-bus power system under different operating conditions such as three-phase short-circuit faults along with changes in loads. Simulation results are then compared with those of a similar controller where there is no coordination between the excitation and steam-valve controllers as well as with a coordinated sliding-mode controller. The results clearly show the effectiveness and superiority of the proposed control scheme.