The inertial range structure of turbulence obeying the Gross-Pitaevskii equation, the equation of motion for quantum fluids, is analyzed by means of a spectral closure approximation. It is revealed that, for the energy-transfer range, the spectrum of the order parameter field ψ obeys k −2 law for k ≪ k * and k −1 law for k ≫ k * , where k * is the wavenumber where the characteristic time scales associated with linear and nonlinear terms are of the same order. It is also shown that, for the

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... cle-numbertransfer range, the spectrum obeys k −1 law for k ≪ k * ,n and k −1/3 law for k ≫ k * ,n , where k * ,n is the wavenumber corresponds to k * in the particle-number-transfer range.