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The literature on immigration and health has provided mixed evidence on the health differentials between immigrants and citizens, while a growing body of evidence alludes to the unhealthy assimilation of immigrants. Relying on five different health measures, the present paper investigates the heterogeneity in health patterns between immigrants and citizens, and also between immigrants depending on their country of origin. We use panel data on more than 100,000 older adults living in nineteen European countries. Our panel data methodology allows for unobserved heterogeneity. We document the existence of a healthy immigrant effect, of an unhealthy convergence, and of a reversal of the health differentials between citizens and immigrants over time. We are able to estimate the time threshold after which immigrants’ health becomes worse than that of citizens. We further document some heterogeneity in the convergence of health differentials between immigrants and citizens in Europe. Namely, the unhealthy convergence is more pronounced in terms of chronic conditions for immigrants from low-HDI countries, and in terms of self-assessed health and body-mass index for immigrants from medium- and high-HDI countries.