When the massive component in a close binary system evolves to fill its Roche lobe, mass transfer occurs and gas is accreted onto the companion star. Recently, the response of the unevolved secondary to accretion has been studied by a number of authors, but the emphasis has been on relatively massive stars which have a radiative envelope (Ulrich and Burger 1976; Flannery and Ulrich 1977; Kippenhalm and Meyer-Hofmeister 1977; Neo et al. 1977). The results show that the mass accepting star becomes overluminous and grows in radius until rapid mass transfer ultimately brings the two stars into contact. Such changes in the structure are caused by the steep increase in the specific entropy in the outermost layers and only a small amount of mass (about a tenth of the initial mass of the star) is accreted before contact is made. Thereafter, the expansion of the common envelope will lead to mass loss from the system. It is also found that, for a given accretion rate, the radial increase is much more conspicuous for a smaller mass star.