We investigate adsorption of a model symmetric binary mixture, exhibiting demixing in a bulk phase, in slitlike pores by using a density functional approach. Our focus is on the evaluation of the first-order phase transitions between adsorbed phases and lines delimiting mixed and demixed adsorbed phases. The scenario for phase changes is sensitive to the pore width and to the energy of adsorption. Both these parameters can qualitatively change the phase behavior of the confined fluid. In particular, for relatively wide pores and for strong wall-fluid interactions, a demixing line can precede the first-order transition. Moreover, a competition between layering type behavior and demixing within particular layers also can lead to further complications of the phase diagram, reflected by the presence of consecutive branches, describing the equilibrium between different adsorbed phases. (C) 2003 American Institute of Physics.