The Doppler effect in doubly double negative acoustic media is theoretically investigated. The radiation spectra of a source moving relative to a medium are calculated with the help of the method of the Green’s functions. It is shown that several Doppler modes can be generated by a monochromatic source owing to the strong dependence of the wave number on frequency. The dependence of the width of the opacity band on the velocity of the relative motion of the source and medium is analyzed.