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The physisorption and chemisorption of hydrogen on two types of Y-junction carbon nanotubes(Y-(6,6) and Y(10,0)) have been studied using molecular dynamics (MD) simulations and semiempirical (AM1) method. The MD simulations study show that H2 molecule can penetrate into the open ends of the branches and stay inside even at room temperature, which is confirmed by the study of potential energies for different pathways with AM1 method. Furthermore, the potential energy variation of H2 penetrating into the open end along the axis of one branch arm is quite similar to that of H2 in straight carbon nanotubes. The study of chemisorption of hydrogen atoms on Y (6,6) indicates that the carbon atoms in the heptagons are more active to bind hydrogen atoms. It has been also found that the neighboring carbon atoms of Y (6,6) prefer to bind two hydrogen atoms.