Abstract The solubility of hydrogen has been determined between about 700 and 1250 K in the austenitic phase of the TiNi 0.8Cu 0.2 and TiNi 0.6Cu 0.4 shape memory alloys for hydrogen contents n H ( n H = H/f.u.) ≤ 0.048. The solubility was found to obey the Sieverts law and decrease with increasing the copper content; the values of the partial molar enthalpy and partial molar non-configurational entropy of solution per mole of hydrogen are: Δ H H 0 = − 28 ± 2 ( kJ/mol ) ; Δ S H nc = − 80 ± 2 ( J/mol K ) ( TiN i 0.8 C u 0.2 ) Δ H H 0 = − 31 ± 3 ( kJ/mol ) ; Δ S H nc = − 88 ± 4 ( J/mol K ) ( TiN i 0.6 C u 0.4 ) The chemical diffusion coefficient D c of H was determined for the TiNi 0.8Cu 0.2 alloy by fitting the isothermal pressure versus time absorption curves to a relationship derived from the second Fick's equation for diffusion. The data for D c are in good agreement with those of the Einstein diffusion coefficient D E prior determined by the Snoek anelastic relaxation peak due to hydrogen. The activation energy W and the pre-exponential factor D o deduced from the composite Arrhenius plot of the absorption and Snoek relaxation data for the TiNi 0.8Cu 0.2 alloy are: W = 0.53 ± 0.02 eV, D o = (3 ± 2) × 10 −7 m 2/s. A comparison of the present results with those available for other NiTiCu alloy compositions shows a gradual decrease of D c with increasing the copper content x from 0 to 0.4.