The evolution of a star of initial mass 9 M_s, and Z = 0.02 in a Close Binary System is followed in the presence of different mass companions in order to study their influence on the final evolutionary stages and, in particular, on the structure and composition of the remnant components. We study two extreme cases. In the first one the mass of the secondary is 8 M_s, whereas in the second one the mass was assumed to be 1 M_s. For the first of those cases we have also explored the possible outcomes of both conservative and non-conservative mass-loss episodes. During the first mass transfer episode, several differences arise between the models. The system with the more extreme mass ratio is not able to survive the 1st. Roche lobe overflow, and spiral-in of the secondary onto the envelope of the primary is most likely. The system formed by two stars of comparable mass undergoes two mass transfer episodes in which the primary is the donor. We have performed two sets of calculations corresponding to this case in order to account for conservative and non-conservative mass transfer during the first mass loss episode. One of our main results is that for the non-conservative case the secondary becomes a Super-AGB. Such a star undergoes a final dredge-up episode, similar to that of a single star of comparable mass. The primary components do not undergo a Super-AGB phase, but instead a carbon-oxygen white dwarf is formed in both cases, before reversal mass transfer occurs. However, given the extreme mass ratios at this stage between the components of the binary system, the possibility of merger episodes remains likely. We also discuss the presumable final outcomes of the system and possible observational counterparts.