The parallel-field magnetoresistance of the accumulation layers formed at the interface between n-Hg,_,Cd,Te with x=0.2 and x=0.3 and an anodic oxide film has been studied as a function of total surface carrier density. The surface carrier density was varied using a persistent negative photoconductivity, with a lifetime in excess of hours at 77 K, caused by excitation of electrons across the anodic oxide band gap (around 3.4 eV): the electrons then recombine with ionised deep traps in the oxide. A series of strong oscillations, known as the 'diamagnetic Shubnikov-de Haas effect' (DSDH) and corresponding to the depopulation of the surface sub-bands, were observed in the parallel-field magnetoresistance. With the comprehensive data obtained in this work, and the re-interpretation of several previous results from different systems, we have been able to show that these oscillations in any accumulation-layer-type system occur at well defined fields as a function of total surface carrier density and thus that the DSDH is a remarkably 'universal' effect.