Coulomb-excitation studies have been performed on the ytterbium isotopes 171 and 173, using oxygen ions with energies up to 55 MeV. Resulting de-excitation gamma rays have been observed in coincidence with back-scattered particles with a NaI(Tl) detector, and as singles spectra with a Ge(Li) detector. Gamma rays which are assigned to transitions within the ground-state rotational bands up to and including the 13/2 level are as follows: 171Yb, 67.2, 76.4, 154.8, 164.0, 170.7, 240.0, 256.6, and 262.0 keV; 173Yb, 78.3, 100.3, 122.3, 143.7, 178.6, 222.5, and 265.9 keV. The following weak gamma rays were also observed: 171Yb, 85.0, 109.0, and 194.0 keV; 173Yb, 272.7, 286.0, and 637.0 keV. M1 transition rates between rotational states were determined from branching ratios, with the assumption that the rotational-model values for the relative E2 transition rates are correct. Agreement with the theory was found within the experimental error. For both nuclei a comparison has been made between experimentally determined values for the parameters describing the intrinsic state and those calculated using the Nilsson wave functions. Excellent agreement is obtained if the spin gyromagnetic ratio for the free nucleon is replaced by an effective value gS,eff. In the case of 171Yb, the agreement of three independent determinations of gS,eff appears to provide further evidence that the concept of replacing the free particle gS by an effective value is valid.