Abstract Rapidly evolving pathogens, such as viruses and bacteria, accumulate genetic change at a similar timescale over which their epidemiological processes occur, such that it is possible to make inferences about their infectious spread using phylogenetic time-trees. For this purpose it is necessary to choose a phylodynamic model. However, the resulting inferences are contingent on whether the model adequately describes key features of the data. Model adequacy methods allow formal rejection of a model if it cannot generate the main features of the data. We present TreeModelAdequacy (TMA), a package for the popular BEAST2 software, that allows assessing the adequacy of phylodynamic models. We illustrate its utility by analysing phylogenetic trees from two viral outbreaks of Ebola and H 1 N 1 influenza. The main features of the Ebola data were adequately described by the coalescent exponential-growth model, whereas the H 1 N 1 influenza data was best described by the birth-death SIR model.