We present the first solution to the problem of estimation of the state of multimachine power systems with lossy transmission lines. We consider the classical three-dimensional \fluxdecay" model of the power system and assume that the active and reactive power as well as the rotor angle and excitation voltage at each generator is available for measurement|a scenario that is feasible with current technology. The design of the observer relies on two recent developments proposed by the authors: a parameter estimation based approach to the problem of state estimation and the use of the dynamic regressor extension and mixing technique to estimate these parameters. Thanks to the combination of these techniques it is possible to overcome the problem of lack of persistent excitation that stymies the application of standard observer designs. Simulation results illustrate the performance of the proposed observer.