In order to reduce the heat flux entering the divertor, it is desirable to have strong impurity radiation in the scrape-off layer (SOL) of reactor-size tokamaks like the International Thermonuclear Experimental Reactor [International Thermonuclear Experimental Reactor (ITER) Conceptual Design Activity Final Report, ITER Documentation Series No. 16 (International Atomic Energy Agency, Vienna, 1991)]. Under such circumstances, however, the SOL plasma is likely to be unstable to the radiative condensation instability. In the present paper, an investigation is undertaken to study the effects of edge-localized mode (ELM) activity on this instability. In the linear regime, it is demonstrated that high-frequency (''grassy'') ELM's may parametrically excite acoustic waves. The possibility of nonlinear radiative collapse with concomitant stratification of the plasma is discussed, and solutions describing nonlinear traveling waves are derived in which the plasma goes over from equilibrium state to another. (C) 1995 American Institute of Physics.