Two types of degeneracy effects are discussed in this paper. In the first case, degenerate surfaces on degenerate bulk semiconducting materials are reviewed. It is pointed out that epitaxic thin films are a prerequisite for any reasonable study of this type of substance. Recent work on degenerate lead chalcogenide films have illustrated the need for epitaxic films. The results show that the scattering at the surface is quite specular. Extremely high surface charge densities were generated by oxygen adsorption. It was found that coulombic interactions caused spreading of the surface state levels comparable to the band gap of the semiconductors. A model based on an oxide with high defect densities of ionized oxygen appears more reasonable. In the second case, a degenerate layer is formed on a nondegenerate bulk by means of an external electric field in a metal-oxide-semiconductor field effect transistor (MOSFET) structure. At low temperatures, an n-type inversion layer formed on a (100) p-type silicon MOSFET behaves like a two-dimensional electron gas as shown by Fowler, Fang, Howard and Stiles using Schubnikov-de Hass osculations. Recently, an oscillatory behavior was observed in the gate voltage dependence of the capacitance of a MOSFET in a high magnetic field (> 50 kOe). Potential utility of these measurements is discussed.