We have measured by incoherent quasi-elastic neutron scattering the diffusion coefficient D t of sorbed hydrogen (HD) molecules in the one-dimensional micropore network of AlPO4-5 zeolite. The confined hydrogen phase in such nano-scale cylindrical tubes (diameter φ = 7.3 Å) behaves as a quasi-(1d) fluid phase. At temperature T = 19.5 K, in the medium loading regime (Θ 40%), the translational molecular mobility is quite large, D t = 0.45 • 10 −5 cm 2 s −1 . When increasing Θ, Dt strongly decreases down to 0.03 • 10 −5 cm 2 s −1 (Θ 95%). At lower temperature T = 10.3 K, the HD molecular mobility is still important, Dt = 0.15 • 10 −5 cm 2 s −1 at Θ 40%.