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The assessment of occupational stress is marred by an overwhelming adoption of simplistic research designs that generally fail to represent the complex reality of the occupational stress process. Informed by the theoretical tenants of both the transactional stress model and the job-demands-control–support model, this paper presents a rare simultaneous assessment of how two types of job demands (cognitive and emotional) are both moderated by job control and social support and mediated by coping for the prediction of work engagement and psychological strain over time. Self-report surveys were administered twice over 12 months to a sample of police-service workers and moderated mediation analyses were conducted on the matched sample of N = 2,481 respondents. The results offer support for the process of occupational stress by demonstrating how both accommodation and avoidance coping mediate the job-demands–outcome relationship over time. The results also demonstrate that this stressor-coping-strain process is simultaneously moderated by job support or job control. We found it interesting that this research also demonstrated that the estimation of work engagement was not unduly influenced by the type of job demands these police employees were exposed to.