Thermal stability of anisotropic and isotropic Co alloy thin-film media is investigated. The orientation ratio of CoCrTa(Pt)/Cr media was controlled by the mechanical texture of the NiP/Al substrates. Bulk magnetic properties, delta M curves and time decay of magnetization in the circumferential and radial directions were measured. The maximum magnetic viscosity coefficient calculated from the time decay of magnetization in the circumferential direction was higher than that in the radial direction for a mechanically textured sample, while it was similar in both directions for a non-textured sample. The magnetic viscosity coefficient in the circumferential direction is smaller than that in the radial direction when the reverse field is in the range of the demagnetization field for thin-film recording media. This implies that an anisotropic sample (namely, a sample with a high orientation ratio) will be more thermally stable when it is not exposed to a large external magnetic field.