We report on measurements performed with the broadband variant of Cavity Ring-Down Spectroscopy based on white-light Supercontinuum. Generated by filaments in a quartz block, the Supercontinuum was coupled into the stable optical cavity characterized by a high Q-factor of 104. The ring-down transients of selectively chosen wavelengths were registered sequentially, revealing a difference of their decay times. The demonstrated high precision of decay time measurement (10-4 relative error) opens the perspective for multiwavelength detection of absorbing species with sub ppb (10-9) sensitivity in the unprecedented broad spectral range of Supercontinuum. This is why we intend to call this technique Supercontinuum Cavity Ring-Down Spectroscopy. Finally, we used the Supercontinuum to quantify variations of the wavelength-dependent reflection coefficient of cavity mirrors; as we show, with an absolute accuracy of 10-6.