Absolute concentrations of minor species can be measured by cavity ring-down spectroscopy (CRDS) by analysing the exponential time decay of the CRDS signal. This paper shows that quantitative concentrations can be measured by CRDS using a moderately narrowband multimode dye laser, even though the ring-down decays exhibit a multi-exponential behavior (nonlinear variation of the losses with the absorbance). A model based on Fabry-Perot theory has been developed to fit the multi-exponential decays by taking into account the convolution of the laser lineshape and of the absorption line. From this model, true absorbances, corrected for nonlinear effects, can be obtained, leading to quantitative measurements of concentrations. Using the model, the dynamic range of CRD measurements is increased by a factor of ten. The sensitivity of the technique is shown to be reduced in the region of the thermal gradient, which induces an important increase of the off-resonance losses/pass. The best fractional absorption/pass we could obtain was estimated to be 10 ppm in the flame front and 5 ppm in the burnt gases of a low-pressure premixed flame of methane and air. The sensitivity is greater when the laser is coupled to the TEM00 mode of the cavity. CRD measurements of [CH] performed in two different spectral ranges in the C-X and B-X bands are compared. (C) 2001 by The Combustion Institute.