The apsidal motion of giant binary stars built on two different models is investigated. In the first model an intermediate isothermal zone between the convective core and the radiative envelope is assumed. The internal data for this model are taken from case 4 of the Richardson-Schwarzschild noisewne model as applied to a star of 10 solar masses with R/R0 equal to 58.9. The second-order apsidalmotion coefficient for this case is equal to 0.003059, which gives a value of 3.7 for the effective polytropic index. This agrees well with the apsidal motion as measured by Wood for the F2 giant TX UMa. In the second model a difference in chemical composition between the radiative envelope and the interior is assumed, with the convective core and the intermediate zone having the same chernical composition. The internal data for a star of 10 solar masses and R/R0 equal to 66, as given by Hen and Schwarzschild in case 15, are used. This model leads to an effective index of 4.01.