We construct the spectral function of the Luther - Emery model which describes one-dimensional fermions with gapless charge and gapped spin degrees of freedom. We find a true singularity with interaction dependent exponents on the gapped spin dispersion and a finite maximum depending on the magnitude of the spin gap on a shifted charge dispersion. We apply these results to photoemission experiments on charge density wave systems and discuss the spectral properties of a one-dimensional Mott insulator.