The temperature dependence of the unit cell parameters of two newly identified hexagonal structure clathrate hydrates of hexamethylethane (HME) and 2,2-dimethylbutane (DMB) have been measured by X-ray powder diffraction. The thermal expansion of the two distinct crystallographic axes was found to be inequivalent. However, the coefficients of cubic expansion are comparable to that in the cubic structure I and II hydrates. The larger thermal expansivity in the clathrate hydrates relative to ice is attributed to the weakening of the host lattice due to the internal pressure generated by the rattling motions of the encaged guests.