The structural characteristics of the critically rotating accretor in binaries are investigated during rapid mass transfer. It is found that the accretor is subjected to periodic pulsation due to accretions and rejections of mass and angular momentum. The gainer attempts to attain both hydrostatic and thermal balances. This physical process can cause the thermal structure of the accreting star to fluctuate with a period of similar to 0.19 y. Stellar wind can be enhanced by a factor of similar to 1.25 x 10(4) when the accretor approaches break-down velocity. Surface entropy and density decrease with the increase of the stellar radius due to the fact that rapid rotation leads to a reduction in the number density and surface temperature. The rotational energy has the same trend as stellar radius due to stellar expansion. Surface opacity which is extremely sensitive to surface temperature has an opposite trend to stellar radius. Moreover, the rate of nuclear energy must be adjusted due to mass removal or accretion at the stellar surface.