In view of the recent progress in the detection of narrow and weak absorption lines as provided by the intracavity technique which utilizes lasers with broad homogeneous emission lines, it appears to interesting to investigate also other light sources with regard to their suitability for intracavity spectroscopic measurements. A promising candidate is an optical parametric oscillator (OPO) pumped by a one-mode field and oscillating in several signal and idler modes, since, as will be shown, this light source exhibits a strong competition effect which, as known from the laser, gives rise to a drastic enhancement in detection sensitivity. In this paper, we calculate the enhancement factor utilizing a simple OPO model which takes account of the spontaneous production of signal and idler photons (parametric fluorescence). The result is similar to that for a laser operated such that spontaneous emission is the only mechanism which prevents a mode with higher losses to be extinguished. Moreover, the OPO offers a possibility to perform the measurement at a frequency which is complementary (with respect to the pump frequency) to the frequency of the absorption line to be detected.