Hydrogen motion in beta-Ti1-yVyHx (y = 0.2,0.4,0.6, and 0.8; x approximately 1) alloys was studied by H-1 NMR, with which the temperature and frequency dependences of proton spin-lattice relaxation times (T1) were measured over the temperature range 105-400 K and at frequencies 9, 22.5, 52, and 90 MHz. The temperature dependences of T1 change systematically with the metal composition; with a decrease in the concentration of V, the minimum value of T1 increases and the temperature at which T1 is minimized shifts to the higher-temperature side. These results are analyzed with two-site jumps of a proton between unequal potential wells, in which Brouwer's model is assumed to describe local structure of the alloys. Good agreement between the experimental and calculated T1 values is given by this treatment, unlike the isotropic diffusion model. The following three parameters are used for the calculation: activation energies for Ti and V are E(Ti) = 16 and E(V) = 9.5 kJ/mol, respectively, and the frequency prefactor is tau0 = 1.5 x 10(-11) s for 0.4 less-than-or-equal-to y less-than-or-equal-to 0.8. The obtained E(Ti) and E(V) values agree with those of pure metal hydrides such as TiH(x) and VH(x), respectively.