The Reynolds Intellectual Assessment Scales (RIAS) measures general intelligence and its two main components, verbal and nonverbal intelligence, each comprising of two subtests. The RIAS has been recently standardized in Denmark, Germany, Switzerland, and Spain. Using the standardization samples of the U.S. (n = 2,438), Danish (n = 983), German (n = 2,103), and Spanish (n = 1,933) versions of the RIAS, this study examined measurement invariance across these four language groups for a single-factor structure, an oblique two-factor structure with a verbal and nonverbal factor, and a bifactor structure with a general, a verbal, and a nonverbal factor. Single-group confirmatory factor analysis (CFA) supported the oblique two-factor and bifactor structure for each language group but not the single-factor structure. The bifactor analysis revealed that the general factor accounted for the largest proportion of common variance in each language group, while the amount of variance accounted for by the two specific factors was small and their reliabilities low. Multiple-group CFA supported scalar invariance in both, the oblique two-factor and bifactor structure.