We obtain the spectral functions of a two-velocities Tomonaga-Luttinger liquid at T = 0K in terms of the Appell hypergeometric functions F1 and F2. In the case of SU(N) spin symmetry, the spectral functions can be expressed with the Gauss hypergeometric functions. We discuss the singularities and thresholds of the spectral functions for both the SU(N) invariant case and the general case.