While it has not yet been possible to give a detailed step-by-step treatment of the evolution of a single star from the main sequence to the white-dwarf stage, such a treatment is available for close binary systems. It has been shown that by calculating the evolution including mass exchange in a system of main-sequence stars of small mass and relatively large separation, one can follow the system to its final stage of a white dwarf and a more massive main-sequence star. This type of evolution arises when the original primary has exhausted its central hydrogen content when mass exchange starts, and the mass of its helium core is small enough so that electron degeneracy prevents the ignition of helium.