Markov three-state progressive and illness–death models are often used in biomedicine for describing survival data when an intermediate event of interest may be observed during the follow-up. However, the usual estimators for Markov models (e.g., Aalen–Johansen transition probabilities) may be systematically biased in non-Markovian situations. On the other hand, despite non-Markovian estimators for transition probabilities and related curves are available, including the Markov information in the construction of the estimators allows for variance reduction. Therefore, testing for the Markov condition is a relevant issue in practice. In this paper, we discuss several characterizations of the Markov condition, with special focus on its equivalence with the quasi-independence between left truncation and survival times in standard survival analysis. New methods for testing the Markovianity of an illness–death model are proposed and compared with existing ones by means of an intensive simulation study. We illustrate our findings through the analysis of a data set from stem cell transplant in leukemia.