DNA and RNA can be assayed rapidly and very sensitively by exploiting the enhanced fluorescence of ethidium intercalated into duplex regions. By assaying at different pHs and introducing a heating/cooling cycle, a great many physicochemical aspects of DNA and RNA can be studied avoiding the use of radiolabels, and often giving information not otherwise readily obtainable. Studies are described on duplex DNA which involve measurement of extinction coefficients, cross-linking by chemicals, Cot curve analysis as well as estimation of drug-DNA binding constants. The assays can be adapted to investigate multi-stranded nucleic acid structures. The use of covalently closed circular DNA also allows rapid and extremely sensitive measurements of nicking caused by irradiation or drugs.