In this thesis two sensitive absorption techniques are used for the detection of trace concentrations of two different nitrogen oxides, which are of interest for atmospheric chemistry. These techniques are both based upon the interaction of mid-infrared laser radiation, provided by Quantum Cascade Lasers, with the molecules being studied. The Optical Feedback-Cavity Enhanced Absorption spectroscopy (OF-CEAS) technique combines the path length benefits of an optical cavity with injection locking of the Quantum Cascade Laser with light returned from the optical cavity. This optical feedback creates a comb of intense modes with spacing dependent on the length of the cavity whose intensity variations can be used to retrieve an absorption spectrum of an analyte gas. This thesis provides a novel method for the improvement of the spectral resolution of the spectrometer: by mounting one of the cavity mirrors upon a moveable stage the cavity mode comb can be translated. By interleaving a series of these spectra a higher resolution spectrum can be created . This is shown to give an improvement in the precision of both the concentration and linewidth retrieved from OF-CEAS measurements. The spectrometer showed the capability of detecting nitrous oxide at concentrations found in ambient air and with pressures as low as 10 Torr. The second technique is Faraday Modulation Spectroscopy. This technique which uses the magnetic splitting of ro-vibrational transitions of paramagnetic molecules to produce a sensitive . absorption technique. The magnetic field is modulated at a frequency much greater than that being used for the laser frequency sweeping and the signal is detected at multiples of the modulation frequency. This spectrometer was used for the detection of nitric oxide and showed an improvement in sensitivity relative to direct absorption measurements.