Protonic motion in the layered compound HLa2NbTi2O10.1.5H2O has been studied by various NMR experiments. The H-1 NMR relaxation times T1, T1rho and T2 have been measured as functions of temperature. At 110 K, the rigid-lattice spectrum is observed which consists of a strong central signal flanked on either side by broader wings. From the line shape analysis of the spectrum it is concluded that the protons of the water molecules and the cage protons exist distinctly and do not form H3O+ ions. The signals show motional narrowing beginning at approximately 190 K indicating the onset of protonic diffusion. The relaxation data have been analysed talking into account the layered structure of the material. Magic angle spinning shows a single signal at 4.47 ppm with respect to TMS. The mechanism of protonic motion in HLa2NbTi2O10.1.5H2O is discussed in the light of these NMR results.