The basics properties of the synchronous and asynchronous sigma-delta (ASD) modulators have been described and current state-of-art in sigma-delta modulation applications has been reported. For comparison, the major differences between synchronous and asynchronous SD modulators have been described. Analysis of hysteresis comparator propagation delay influence to the ASD modulator performances has been provided. The mathematical analysis, computer simulations and measurement results confirm the central frequency detoriation due to propagation delay influence. For propagation delay compensation two methods have been proposed. The first method is based on limitation of the integrator output voltage (method 1), which increses ASD central frequency, while second method introduce hysteresis threshold voltage amplitude modulation which keeps the integrator output voltage within calculated hysteresis threshold levels. Based on the mathematical model of the ASD modulator, for simulation purposes of the propagation delay influence and the proposed method for propagation delay compensation (method 1 and method 2), Simulink model in Matlab® has been created. Matlab implementation of the A/D converter circuit for 1-bit ASD signal to synchronous PCM m-bit digital word for voice-band applications has also been proposed. Using Multisim Analog Devices Edition, simulation model of ASD modulator has been applied to class-D power amplifier for method 2 verification. For measurement results, the ASD modulator ciruit has been implemented with possibility for method 1 and method 2 application. The measuerment results on the ASD circuit confirm the mathematical analysis for the propagation delay influence and compensation method contributions which improve ASD modulator performances. For ASD modulator application in class-D power amplifier, total harmonic distorsion has been measured. It has been shown that method 2 implementation reduces total harmonic distorsion of output signal for full range of input signal amplitudes.