Recent concern over possible long term stratospheric changes caused by the introduction of man-made compounds has increased the need for instrumentation that can accurately measure stratospheric minor constituents. The technique of radio spectroscopy at millimeter wavelengths was first used to observe rotational transitions of stratospheric ozone nearly two decades ago, but has not been highly developed until recently. We report here on a ground-based observing technique which employs a millimeter-wave superheterodyne receiver and multichannel filter spectrometer for measurements of stratospheric constituents that have peak volume mixing ratios that are < 10−9, more than 3 orders of magnitude less than that for ozone. We have used the technique for an extensive program of observations of stratospheric chlorine monoxide and also for observations of other stratospheric trace gases such as 16O3, vibrationally excited 16O3, 18O2 16O, N2O, HO2, and HCN. In the present paper, analysis of the observing technique is given, including the method of calibration and analysis of sources of error. The technique is found to be a reliable means of observing and monitoring important stratospheric trace constituents.