The paper studies large-dimention factor models with nonstationary factors and allows for deterministic trends and factors integrated of order higher then one.We follow the model speci.cation of Bai (2004) and derive the convergence rates and the limiting distributions of estimated factors, facto… rs loadings and common components. We discuss in detail a model with a linear time trend. We ilustrate the theory with an empirical exmple that studies the fluctuations of the real activity of U.S.economy. We show that these .uctuationas can be explained by two nonstationary factors and a small number of stationary factors. We test the economic interpretation of nonstationary factors.