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Saturation spectroscopy of the 2$\nu 3$ band of methane was carried out using an optical cavity absorption cell and a 1.6-$\mu$m-grating feedback external-cavity semiconductor laser. An experimental setup was similar with the pioneering work in the 1.5-$\mu$m region. Since the linewidth of the observed saturation dips was just 0.5 MHz, a high potential exists for the use of this technique for high resolution spectroscopy and double-resonance spectroscopy.