A method of detecting simultaneously acetone and carbon dioxide, and preferably methane, in breath using cavity-enhanced absorption spectroscopy. The method utilises a broadband light source emitting light in the range 1640 to 1700nm such as a superluminescent light emitting diode. The light is coupled into an optical cavity into which the breath sample is admitted and the characteristic spectral features of carbon dioxide, acetone and methane are identified in the absorption spectrum output. Wavelength selectivity can be provided by use of a tunable fibre filter on the input side of the cavity or by an FTIR on the output side. The apparatus is suitable for widespread use as it is relatively portable and durable and it can thus be used for screening for diseases in which the presence of acetone is a marker, such as diabetes.