This paper investigates the persistence in health limitations for individuals within the member states of the European Union. We use the full eight waves of data available in the European Community Household Panel (ECHP) to explore the relative contributions of state dependence, unobserved heterogeneity and socioeconomic characteristics, in particular income, education and activity status, and how these vary across countries. We focus on binary measures of health limitations, constructed from the answers to the question: "Are you hampered in your daily activities by any physical or mental health problem, illness or disability?". Dynamic non-linear panel data models are specified and estimated using both pooled and random effects probit and logit models together with complementary log-log models. The random effects probit specifications are preferred. Results reveal high state dependence of health limitations, which remains after controlling for measures of socioeconomic status. There is heterogeneity in the socioeconomic gradient across countries.