The features of the homogeneous scalar field φ with classical Lagrangian L = φ_;i φ^;i/2 - V(φ) and tachyon field Lagrangian L = -V(φ)√(1–φ_;i φ^;i) causing the observable accelerated expansion of the Universe are analyzed. The models with constant equation-of-state parameter w_de = p_de/ρ_de < -1/3 are studied. For both cases the fields φ(a) and potentials V(a) are reconstructed for the parameters of cosmological model of the Universe which are derived from observations. The effect of rolling down of the potential V(φ) to minimum is shown.