The robust transient stabilisation problem (with stability proof) of a synchronous generator in an uncertain power network with transfer conductances is rigorously formulated and solved. The generator angular speed and electrical power are required to be kept close, when mechanical and electrical perturbations occur, to the synchronous speed and mechanical input power, respectively, while the generator terminal voltage is to be regulated, when perturbations are removed, to its pre-fault reference constant value. A robust adaptive nonlinear feedback control algorithm is designed on the basis of a third-order model of the synchronous machine: only two system parameters (synchronous machine damping and inertia constants) along with upper and lower bounds on the remaining uncertain ones are supposed to be known. The conditions to be satisfied by the remote network dynamics for guaranteeing L-2 and L-infinity robustness and asymptotic relative speed and voltage regulation to zero are weaker than those required by the single machine-infinite bus approximation: dynamic interactions between the local deviations of the generator states from the corresponding equilibrium values and the remote generators states are allowed.