Existence and possibility of self-sustained oscillations of acoustoelectric and photoelectric voltages in layered piezoelectric-semiconductor structures without any negative differential conductivity and acoustoelectric domains are demonstrated experimentally and theoretically, A joint experimental study of acoustoelectric and photoelectric phenomena in the same structure permits to establish similar electronic processes. Experimental and theoretical results show that nonlinear acoustoelectric and photoelectric voltages with electronic relaxation properties and external feedback are necessary for observing the phenomena. The theory presented explains the experimental results obtained. A criterion for excitation in a soft mode and dynamic characteristics of the self-sustained oscillations under various external conditions, as temperature, illumination and humidity are discussed. Periodic and stochastic modes of oscillation are noted. The quasi-harmonic mode of oscillations described by the Van der Pol equation is very useful and attractive for practical application because of the fact that the oscillation frequency is proportional to the square root of the relaxation time of electronic processes in semiconductors and that it can be precisely measured and digitized. Due to the precise method presented for measuring the relaxation time, new fundamental possible applications to methods of investigation of physical and chemical sensors with a frequency output are noted.