We have used high-resolution neutron powder diffraction to study the phase diagram of LaNi5Dx at temperatures up to 100°C. Diffraction patterns were recorded during consecutive absorption–desorption cycles at 100, 65 and 30°C. In a sequence of four patterns taken during desorption at 100°C, we observed the β phase transforming continuously to the γ phase: the first pattern was 100% β phase; the fourth one was 100% γ phase; the second and third patterns were also single phase, but had lattice parameters intermediate between those of the β and γ phases. The succeeding γ→α transformation remained discontinuous, that is, co-existing γ and α phases were observed via two diffraction patterns with distinct lattice parameters. The following absorption–desorption cycle was conducted at 65°C. Again, the β→γ transformation was continuous. In the final cycle, conducted at 30°C, the β→γ transformation was discontinuous. Hence, there appears to be a thermodynamic critical point of the β+γ phase ‘equilibrium’ in this sample, between 65 and 30°C. This is the first such observation in the LaNi5–H/D system. The pressure–composition isotherms resemble those of a Mm(NiCoMnAl)5 battery alloy in that a considerable fraction of the D capacity appears to lie within the concentration range of the ‘hydride phase’.