We have developed a novel optical setup which is based on a high finesse cavity and absorption laser spectroscopy in the near-IR spectral region. In pilot experiments, spectrally resolved absorption measurements of biomarkers in exhaled breath, such as methane and acetone, were carried out using cavity ring-down spectroscopy (CRDS). With a 172-cm-long cavity, an efficient optical path of similar to 132 km was achieved. The CRDS technique is well suited for such measurements due to its high sensitivity and good spectral resolution. The detection limits for methane of similar to 8 ppbv and acetone of similar to 2.1 ppbv with spectral sampling of 0.005 cm(-1) were achieved, which allowed to analyze multicomponent gas mixtures and to observe absorption peaks of (CH4)-C-12 and (CH4)-C-13. Further improvements of the technique have the potential to realize diagnostics of health conditions based on a multicomponent analysis of breath samples.