A method is given to calculate the line structure of vibronic bands for a given coupling function p (s), which latter incorporates the frequency and equilibrium change of the oscillator s. The form of the single lines is generally given in terms of their moments. For the important case, where p (s) decomposes into a sum of Gaussian or Lorenzian functions, the line functions are written explicitly. In absorption the lines must appear above the low-energy part of the background. In emission the opposite is true. Other features are also explained. The theory is restricted to T=0, yet can be easily extended to finite, but low temperatures (at higher temperatures there is no vibronic structure).