Influenza A viruses have caused a number of global pandemics, with considerable mortality in humans. Here, we analyse the time periods between influenza pandemics since 1700 under different assumptions to determine whether the emergence of new pandemic strains is a memoryless or history-dependent process. Bayesian model selection between exponential and gamma distributions for these time periods gives support to the hypothesis of history-dependence under eight out of nine sets of modelling assumptions. Using the fitted parameters to make predictions shows a high level of variability in the modelled number of pandemics from 2010-2110. The approach we take here relies on limited data, so is uncertain, but it provides cheap, safe and direct evidence relating to pandemic emergence, a field where indirect measurements are often made at great risk and cost.