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Background Markov models are used in health research to simulate health care utilization and disease states over time. Health phenomena, however, are complex, and the memoryless assumption of Markov models may not appropriately represent reality. This tutorial provides guidance on the use of Markov models of different orders and stratification levels in health decision-analytic modeling. Colorectal cancer (CRC) screening is used as a case example to examine the impact of using different Markov modeling approaches on CRC outcomes. Methods This study used insurance claims data from commercially insured individuals in Oregon to estimate transition probabilities between CRC screening states (no screen, colonoscopy, fecal immunochemical test or fecal occult blood test). First-order, first-order stratified by sex and geography, and third-order Markov models were compared. Screening trajectories produced from the different Markov models were incorporated into a microsimulation model that simulated the natural history of CRC disease progression. Simulation outcomes (e.g., future screening choices, CRC incidence, deaths due to CRC) were compared across models. Results Simulated CRC screening trajectories and resulting CRC outcomes varied depending on the Markov modeling approach used. For example, when using the first-order, first-order stratified, and third-order Markov models, 30%, 31%, and 44% of individuals used colonoscopy as their only screening modality, respectively. Screening trajectories based on the third-order Markov model predicted that a higher percentage of individuals were up-to-date with CRC screening as compared with the other Markov models. Limitations The study was limited to insurance claims data spanning 5 y. It was not possible to validate which Markov model better predicts long-term screening behavior and outcomes. Conclusions Findings demonstrate the impact that different order and stratification assumptions can have in decision-analytic models. Highlights This tutorial uses colorectal cancer screening as a case example to provide guidance on the use of Markov models of different orders and stratification levels in health decision-analytic models. Colorectal cancer screening trajectories and projected health outcomes were sensitive to the use of alternate Markov model specifications. Although data limitations precluded the assessment of model accuracy beyond a 5-y period, within the 5-y period, the third-order Markov model was slightly more accurate in predicting the fifth colorectal cancer screening action than the first-order Markov model. Findings from this tutorial demonstrate the importance of examining the memoryless assumption of the first-order Markov model when simulating health care utilization over time.