Background: The Job Demands-Resources Theory (JD-R) is one of the most influential theoretical frameworks for explaining work engagement. The JD-R postulates the existence of a health impairment process in which job demands lead to strain, and of a motivational process in which job resources lead to work engagement. Although cognitive functions are among the most important characteristics of employees related to job, still little is known about its moderating role in JD-R processes; hence in this study we make a novel attempt to test the invariance of JD-R propositions among employees at different levels of cognitive functioning. Material and Methods: A group of 383 multioccupational employees completed a set of questionnaires measuring job resource: co-worker support, supervisor support, performance feedback; job demands: emotional demands, occupational constraints, work-home interferences; Utrecht Work Engagement Scale; Oldenburg Burnout Inventory along with 2 working memory and 3 fluid intelligence tests. Results: The multigroup invariance analysis with latent variables revealed that both the health impairment process and the motivational process as postulated by JD-R are invariant across groups of employees with either high or low levels of fluid intelligence and working memory capacity. Conclusions: This result provides the first piece of evidence for JD-R robustness among employees at different levels of cognitive functioning. Our findings counterintuitively suggest that employees with high cognitive functioning are not more resistant to job demands than employees with low cognitive functioning and that in order to be work-engaged they need job resources, no less than their colleagues with low cognitive functioning.