This article describes simultaneous rheological and small-angle X-ray scattering (SAXS) studies of complex fluids, using a modified rheometer that allows in situ synchrotron SAXS measurements. We investigated the behavior under shear stress of lamellar liquid-crystalline suspensions, recently reported, comprised of covalent mineral sheets of H3Sb3P2O14 in water, that form sols and gels. Two original nematic mineral suspensions of HSbP2O8 disklike and H4Nb6O17 rodlike nanoparticles were also examined. We correlate both the existence of a yield stress and a strong decrease in viscosity (shear-thinning behavior) with textural changes easily detected by SAXS. The exact nature of the phase (nematic or lamellar) does not seem to affect such phenomena as long as there is orientational order. Moreover, strongly flow-birefringent and shear-thinning isotropic suspensions of anisotropic nanoparticles displayed very anisotropic SAXS patterns under shear.