Different ungulate species that co-occur over evolutionary time have been hypothesized to develop mechanisms to limit the degree to which they directly compete for the same limited resources (i.e. resource partitioning). In situations where an exotic ungulate has been recently introduced to a system, resource partitioning has not likely developed; this appears to be the situation between introduced feral ass Equus asinus and indigenous mountain sheep Ovis canadensis in the Sonoran Desert of southeastern California, USA. We analysed data from aerial surveys conducted during 1993–2003 to look for evidence of an effect of feral ass abundance on mountain sheep demography. After controlling for the influence of forage availability via rainfall, we found no evidence of relationship between an index of feral ass abundance and indices of reproduction or recruitment in mountain sheep (P≥0.360). However, we found strong evidence for an effect on indices of sheep abundance and population rate of change. There was an interactive effect of rainfall and feral ass, such that a negative relationship between abundances of mountain sheep and feral ass was strongest during the driest years (P=0.014). There was a negative relationship between rate of change for sheep populations and feral ass abundance (P=0.016), which was not affected by rainfall. These results indicated a competitive effect of feral ass on mountain sheep populations, but the mechanism of competition remains unclear. Further research should use manipulations in feral ass abundance to clarify interactions between these species.