► We tested whether there was a general factor of personality (GFP) in chimpanzees, orangutans, or rhesus macaques. ► In each of these species we tried extracting a GFP using confirmatory factor analysis (CFA) and two principal axis factor analyses (PFA). ► If a GFP exists, we would expect good model fit, loadings consistent with a GFP, and/or two correlated higher-order factors. ► We found no evidence of a GFP in chimpanzees, orangutans, or rhesus macaques. We examined whether a general factor of personality (GFP) was present in chimpanzees, orangutans, or rhesus macaques. We used confirmatory factor analysis (CFA) to model correlations among first-order factors as arising from a GFP. We then conducted principal axis factor analyses (PFA) of the first-order factors to extract a single higher-order factor and then to extract two oblique higher-order factors. The CFA model fit was poor for chimpanzees and orangutans, but not rhesus macaques. The single higher-order factors extracted via PFA did not resemble the GFP in all three species. The oblique higher-order factors extracted via PFA were only weakly correlated in all three species. These results do not support the existence of a GFP in nonhuman primates.