The dark energy transition between quintessence (w > −1) and phantom (w < −1) regimes (the crossing of the cosmological constant boundary) is studied using the dark energy equation of state. Models characterized by this type of transition are explicitly constructed and their equation of state is found to be implicitly defined. The behavior of the more general models with the implicitly defined equation of state, obtained by the generalization of the explicitly constructed models, is studied to gain insight into the necessary conditions for the occurrence of the transition, as well as to investigate the mechanism behind the transition. It is found that the parameters of the generalized models need to satisfy special conditions for the transition to happen and that the mechanism behind the transition is the cancellation of the contribution of the cosmological constant boundary. The aspects of the behavior of the generalized models which are not related to the transition are briefly discussed and the role of the implicitly defined dark energy equation of state in the description of the dark energy evolution is emphasized. One of the most important aspects of the present universe is its accelerated expansion. Numerous and complementary cosmological observations such as supernovae of the type Ia (SNIa) [1], the anisotropies of the cosmic microwave background radiation (CMBR) [2], large scale structure (LSS) [3], and others seem to reconfirm this characteristic of the small-redshift evolution of the universe with the arrival of each new set of cosmological data. Although the present acceleration of the universe expansion is well established observationally, the nature of the cause of the cosmic acceleration is much more uncertain. A large number of models assume the existence of the component of the universe with the negative pressure, named dark energy [4], which at late times dominates the total energy density of the universe and accelerates its expansion. Models of dark energy differ with respect to the size of the parameter w = p d /ρ d (p d and ρ d are the pressure and energy density of dark energy, respectively 1 ) of their equation of state (EOS) as well as the variation of the parameter w with redshift or cosmic time. The cosmological constant (CC), with w = −1, occupies the central place among the dark energy models, both in theoretical considerations and in data analysis [5]. The conceptual difficulties in the understanding of the measured size of the CC and its relation to other cosmological parameters motivated the study of the dynami- * On leave of absence from the Theoretical Physics Division, Rudjer Bošković Institute, Zagreb, Croatia. † Electronic address: stefancic@ecm.ub.es 1 Since only the dark energy component of the universe will be discussed furtheron, in the remainder of the paper the subscript d will be dropped.cal models of CC (such as renormalization group running models of CC and other relevant cosmological parameters [6,7,8,9]) and dynamical models of dark energy in general. The models of d...