An algorithm is proposed to estimate the parameters of transmission lines and transformers using synchronized phasor measurements at both ends of the element. It uses a simultaneous state and parameter estimation algorithm applied to an artificial system to find the parameters of the line or transformer. A number of successive data sets can be used to improve the accuracy of the estimation. The method can be combined with a resampling scheme to obtain very accurate values of constant parameters. It is also shown that this algorithm can track the values of time-varying parameters, including sudden changes resulting from line compensation or tap changing. The performance of the algorithm was tested by estimating all the parameters of the IEEE 30 bus test system, including one parameter that changes with time.