The linear coefficient of thermal expansion of β′-AgMg has been determined from 77° to 800°K by means of lattice-parameter measurements below room temperature and dilatometric measurements at higher temperatures. At room temperature, the linear coefficient of thermal expansion was found to be 21×10−6 per °C. The Grüneisen parameter derived from the coefficient of thermal expansion obtained here and from other thermal data available in the literature is essentially constant (γ≃1.8) above the Debye temperature, but increases at lower temperatures. Using Slater's formula, a value of 2.2 was obtained for the Grüneisen parameter at 0°K.