We report the results of a high resolution x-ray scattering study of the structure of two high Tc oxides as a function of temperature. In contrast to our results on YBa2Cu3O7, we find no evidence for a structural distortion near the superconducting transition in La1.85Sr.15CuO4. We also find that YBa2Cu2.88Co.12O7 is tetragonal from 300 K to 14K (i.e. both above and below the superconducting transition) to within 5 parts in 104. The significance of these results for theories of high temperature superconductivity is discussed. © 1988.