The spectrum of two-point functions in a holographic renormalization group flow from an ultraviolet (UV) to an infrared (IR) conformal fixed point is necessarily continuous. For a toy model, the spectral function does not only show the expected UV and IR behaviours, but other interesting features such as sharp peaks and oscillations in the UV. The spectral functions for the SU(3) × U(1) flow in AdS₄/CFT₃ and the SU(2) × U(1) flow in AdS₅/CFT₄ are calculated numerically. They exhibit a simple cross-over behaviour and reproduce the conformal dimensions of the dual operators in the UV and IR conformal phases.