Photon-dominated regions (PDRs) are powerful molecular line emitters in external galaxies. They are expected in galaxies with high rates of massive star formation due to either starburst (SB) events or starburst coupled with active galactic nuclei (AGN) events. We have explored the PDR chemistry for a range of physical conditions representing a variety of galaxy types. Our main result is a demonstration of the sensitivity of the chemistry to changes in the physical conditions. We adopt crude estimates of relevant physical parameters for several galaxy types and use our models to predict suitable molecular tracers of those conditions. The set of recommended molecular tracers differs from that which we recommended for use in galaxies with embedded massive stars. Thus, molecular observations can in principle be used to distinguish between excitation by starburst and by SB+AGN in distant galaxies. Our recommendations are intended to be useful in preparing Herschel and ALMA proposals to identify sources of excitation in galaxies.