We use ab initio molecular dynamics simulations to study the adsorption of thin water films with 1 and 2 ML coverage on anatase TiO2 (001) nanotubes. The nanotubes are modeled as 2D slabs, which consist of partially constrained and partially relaxed structural motifs from nanotubes. The effect of anion doping on the adsorption is investigated by substituting O atoms with N and S impurities on the nanotube slab surface. Due to strain-induced curvature effects, water adsorbs molecularly on defect-free surfaces via weak bonds on Ti sites and H bonds to surface oxygens. While the introduction of an S atom weakens the interaction of the surface with water, which adsorbs molecularly, the presence of an N impurity renders the surface more reactive to water, with a proton transfer from the water film and the formation of an NH group at the N site. At 2 ML coverage, a further surface-assisted proton transfer takes place in the water film, resulting in the formation of an OH- group and an NH2+ cationic site on the surface.