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Abstract The subtype composition of seasonal influenza waves varies in space and time. Influenza subtypes A/H1N1, A/H3N2 and B tend to have different impacts on population groups; therefore, understanding the drivers of their cocirculation and anticipating their composition is important for epidemic preparedness. FluNet provides data on influenza specimens by subtype for more than 150 countries. However, owing to surveillance variations across countries, global analyses usually focus on subtype compositions, a kind of data difficult to treat with advanced statistical methods. We used compositional data analysis to circumvent the problem and study trajectories of annual subtype compositions of countries. Here we first examine global trends from 2000 to 2023. We identify a few seasons which stood out for the strong within-country subtype dominance due to either a new virus/clade taking over (2003/2004 season, A/H1N1pdm pandemic) or subtypes’ spatial segregation (coronavirus disease 2019 pandemic). Second, we show that geographical factors, most notably international mobility, concurred in shaping countries’ composition trajectories between 2010 and 2019. Trajectories clustered in two macroregions characterized by subtype alternation versus persistent mixing. Finally, we define five algorithms for forecasting the next year’s composition and found that incorporating the global history of subtype composition in a Bayesian hierarchical vector autoregressive model improved predictions compared with naive methods. The joint analysis of spatiotemporal dynamics of influenza subtypes worldwide reveals a hidden structure in subtype circulation that can be used to improve predictions of the subtype composition of next year’s epidemic according to place.