A "refugee crisis" has caught Europe by surprise in 2015. This article seeks to integrate the influence of the crisis into models of the electoral success of populist radical right parties. The overarching research question is whether we can observe a "fourth wave" of populism. The theoretical argument rests on existing demand- and supply-side explanations, but emphasizing the electoral trajectories of parties as well as the shock of the crisis. Empirically, the electoral results of 16 populist radical right parties at 50 elections between 2000 and mid-2017 in 12 countries are studied. The modelling strategy involves party-specific non-linear latent curves. Results indicate that net of the "refugee crisis", a slowing down or downward trend of populist parties' electoral results might be observed. Sparse data and the hypothetical prediction limits the findings, though.