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Summary form only given. Cavity ringdown laser absorption spectroscopy (CRDS) is a sensitive, accurate way to acquire weak optical absorption spectra. Monochromatic light is multiply reflected within a high-finesse optical cavity containing the absorbing medium of interest and the energy loss rate (the inverse of ringdown time) is recorded. For sufficiently weak absorption, the ringdown rate increases linearly as absorbance of the medium. High-quality mirrors that are commercially available yield ringdown times of a few microseconds, resulting in a very long effective absorption path length for CRDS. Moreover, the ringdown time is usually independent of light intensity, so that sensitivity is not limited by optical intensity. We use a rapidly swept optical cavity and a CW single-mode tunable diode laser to record high-resolution CRDS of weak combination bands (e.g., carbon dioxide or acetylene in the 1.55-/spl mu/m near-infrared region). Our approach simplifies CW-CRDS by eliminating the need for a fast optical switch or for cavity locking. It depends on understanding the dynamic response and characteristic ringing effects associated with the build-up and decay of radiation in a high-finesse optical cavity as its length is scanned piezoelectrically by an applied linear voltage ramp. We employ a combination of CRDS and cavity-enhanced absorption spectroscopy, to compensate for nonlinear CRDS response that is observed for stronger absorption features. Experimental results, performance characteristics and numerical simulations are presented.