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We investigate the late-time evolution of the Universe within a cosmologicalmodel in which dark matter and dark energy are identified with two interactingscalar fields. Using methods of qualitative analysis of dynamical systems, weidentify all cosmological solutions of this model. We show that viablesolutions -- in the sense that they correspond to a cosmic evolution in which along enough matter-dominated era is followed by a current era of acceleratedexpansion -- can be found in several regions of the parameter space. Thesesolutions can be divided into two categories, namely, solutions that evolve toa state of everlasting accelerated expansion, in which the energy density ofthe dark-matter field rapidly approaches zero and the evolution becomesentirely dominated by the dark-energy field, and solutions in which the stageof accelerated expansion is temporary and the ratio between the energydensities of dark energy and dark matter tends, asymptotically, to a constantnonzero value.

Late-time evolution of the Universe within a two-scalar-field cosmological model