This dissertation is concerned with high accuracy measurements of AC signals and electrical power. The introduction contains a short survey of the current stage in that field of metrology and also reveals advantages and disadvantages of the existing measurement methods. The main stress is on the measurements applying thermal converters and time division multipliers, as already long used and proven methods, while the sampling method developed in German PTB, although the most similar one to our method, is only briefly described. That method can be objectively evaluated and compared with our method only after adoption of the theoretical basis, which is systematically studied throughout the whole text, so such discussions were left for the end of the whole dissertation. The first chapter begins with the treatise of the technical limits that strongly influence the abilities of sampling methods, followed by explanation of specifics of our manner of sampling in comparison with the most frequently used ones. In continuation, the detailed discussion on theoretical basis of our method for measurement of spectrally clean sinusoid signal, assuming the perfect sampling, is carried out, as well as a number of computer simulations in order to estimate the highest reachable accuracy. After thorough evaluation of the simulation results, the theory is extended to the real measurements, taking into account all predictable imperfections of sampling. Accuracy of suggested calculating procedure is again estimated by computer simulation, and as the final proof of worthiness of theoretical thesis, the results of a series of real measurements in the Primary Electromagnetic Laboratory of the Faculty of Electrical Engineering and Computing in Zagreb are given, which clearly show that the measurement uncertainty for measurements of amplitude of sinusoid signal in laboratory conditions does not exceeds 5 ppm (with the measurement uncertainty extension factor k = 2 applied). The rest of first chapter introduces spectral analysis as further development of the theoretical basis of our method, so that it can be used also in measurements of signals composed of many harmonics, again following the sequence of explanation from theoretical basis, over computer simulations to the real measurements. Here, the theory of discrete time signal processing is applied, first of all the Discrete Time Fourier Transform and digital filtering, but in conjunction with the previously developed method for measurement of spectrally clean sinusoid signal. Computer simulations, as well as experiments in PEL have proven an extraordinary accuracy of this method, that is, only a little higher measurement uncertainty than for the measurement of clean sinusoid, i.e. about 10 ppm (k = 2). Second chapter is devoted to the power measurement. At the beginning, an improvement of the method introduced in the first chapter is described, which enables that method to be applied also in measurement of the phase, i.e. phase difference between two signals. Improved in that way, this method becomes completely finished and suitable for power measurement. Besides enabling it to measure phase difference, the last development resulted with advance in calculation of signal parameters, so all relevant parameters can be calculated with almost equal accuracy. Uncertainty of phase difference is about 8 ppm (k = 2), what is proven with a series of experiments in PEL. Finally, suitability of that method for power measurement is considered. Basically, three different measurement systems are proposed and their similarities, as well as differences noticed. Also, an objective comparison with the PTB’s solution is provided. Trial experiments, using relatively inappropriate equipment, justified our assumptions about relatively high reachable accuracy of proposed measurement systems and method, because already in these first measurements an uncertainty of about fifteen ppm was obtained.