We demonstrate the generation of quasi-continuous ultraviolet excitation at wavelengths shorter than 240 nm using the frequency-doubled output of a synchronously pumped picosecond dye laser operating in the region of 420 nm. Owing to the relatively low peak power but high average power of the system, we obtain high-quality resonance Raman spectra at wavelengths as short as 209 nm. We apply the source to the study of the binding of anticancer drugs to DNA. In particular, we compare the binding of cis-diamminedichloroplatinum (II) (cisplatin) and cis-diammine-1, 1-cyclobutane dicarboxylate platinum (II) (carboplatin) to certain mononucleotides.