BACKGROUND: Multistate models have been widely applied in health technology assessment. However, extrapolating survival in a multistate model setting presents challenges in terms of precision and bias. In this article, we develop an individual-level continuous-time multistate model that integrates relative survival extrapolation and mixed time scales. METHODS: We illustrate our proposed model using an illness-death model. We model the transition rates using flexible parametric models. We update the hesim package and the microsimulation package in R to simulate event times from models with mixed time scales. This feature allows us to incorporate relative survival extrapolation in a multistate setting. We compare several multistate settings with different parametric models (standard vs. flexible parametric models), and survival frameworks (all-cause vs. relative survival framework) using a previous clinical trial as an illustrative example. RESULTS: Our proposed approach allows relative survival extrapolation to be carried out in a multistate model. In the example case study, the results agreed better with the observed data than did the commonly applied approach using standard parametric models within an all-cause survival framework. CONCLUSIONS: We introduce a multistate model that uses flexible parametric models and integrates relative survival extrapolation with mixed time scales. It provides an alternative to combine short-term trial data with long-term external data within a multistate model context in health technology assessment.