Electronic contributions to the thermoelectric power of a dynamically two-dimensional degenerate electron system in semiconductor inversion and accumulation layers, or other systems that exhibit two-dimensional or quasi-two-dimensional behaviour, are calculated under ionised impurity scattering. In the treatment the authors have also included a two-dimensional gas formed in semiconductor and semimetal films where the quantum size effect (QSE) is predominant. It has been found that the thermoelectric power decreases with the increase of interface carrier concentrations. Finally, results have been compared with recent experimental findings and the magnitude of the observed thermopower actually appears to agree quite well with the theoretical results of this paper.