We demonstrate an experimental method for the accurate measurement of the absorption cross section of transient species, such as organic peroxy radicals in which the concentration of the radicals is determined via the absorption of a stable coproduct that is produced stochiometrically. The requirements for the experimental apparatus, a dual-wavelength cavity ring-down spectrometer, and the chemical protocol for transient species generation are discussed. The capability of this approach is demonstrated by measuring the peak absorption cross section of the ethyl peroxy radical, C2H5O2, whose value for the (A) over tilde <-(X) over tilde electronic transition at 7596 cm(-1) (lambda = 1316.5 nm) is found to be a sigma(EP)(p) = 5.29(20) x 10(-21) cm(2). These present results are compared to those obtained from other methods of measurement of sigma(EP)(p). Possible random and systematic errors are discussed.