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We present an application of cavity-enhanced absorption spectroscopy with an off-axis alignment of the cavity formed by two spherical mirrors and with time integration of the cavity-output intensity for detection of nitrogen dioxide (NO₂) and iodine monoxide (IO) radicals using a violet laser diode at λ=404.278 nm. A noise-equivalent (1σ≡ root-mean-square variation of the signal) fractional absorption for one optical pass of 4.5×10^-8 was demonstrated with a mirror reflectivity of ∼0.99925, a cavity length of 0.22 m and a lock-in-amplifier time constant of 3 s. Noise-equivalent detection sensitivities towards nitrogen dioxide of 1.8×10¹⁰ molecule cm^-3 and towards the IO radical of 3.3×10⁹ molecule cm^-3 were achieved in flow tubes with an inner diameter of 4 cm for a lock-in-amplifier time constant of 3 s. Alkyl peroxy radicals were detected using chemical titration with excess nitric oxide (RO₂+NO→RO+NO₂ …