The collective motion of nucleons from high-energy heavy-ion collisions is analyzed within a relativistic two-fluid model for different equations of state (EoS). As function of beam energy the theoretical slope parameter F_y of the differential directed flow is in good agreement with experimental data, when calculated for the QCD-consistent EoS described by the statistical mixed-phase model. Within this model, which takes the deconfinement phase transition into account, the excitation function of the directed flow left angle P_x right angle turns out to be a smooth function in the whole range from SIS till SPS energies. This function is close to that for pure hadronic EoS and exhibits no minimum predicted earlier for a two-phase bag-model E...