The presence of hydrides is an important factor in assessing the potential for delayed hydride cracking in Zr-2.5Nb alloys, and consequently, the terminal solid solubility (TSS) of hydrogen in the material is an important parameter. In pure zirconium doped with hydrogen, the TSS is marked by a dissolution peak of internal friction on heating and a truncated precipitation peak associated with hydride nucleation on cooling. These phenomena occur only at low frequencies and are accompanied in torsion pendulum studies by autotwisting of the sample (or zero-point drift) that stops abruptly at the TSS. Neither the dissolution/precipitation peaks nor the autotwisting phenomena are observed in Zr-2.5Nb. However, the TSS is also marked by an abrupt change in the slope of Young's modulus as a function of temperature. This phenomenon is observed regardless of the frequency (in the range 1 Hz to 120 kHz) and in both pure zirconium and Zr-2.5Nb alloys. The reasons for the absence of the dissolution/precipitation peak in Zr-2.5Nb alloys are discussed and the use of Young's modulus changes to investigate the TSS of hydrogen and the hysteresis between heat-up and cool-down TSS curves is demonstrated.