We perform n-body simulations for models with a DE component. Besides of DE with constant negative w=p/ρ≥−1, we consider DE due to scalar fields, self-interacting through RP or SUGRA potentials. According to our post-linear analysis, at z = 0, DM power spectra and halo mass functions do not depend on DE nature. This is welcome, as ΛCDM fits observations. Halo profiles, instead, are denser than ΛCDM. For example, the density at 10 h −1kpc of a DE ∼1013 M ⊙ halo exceeds ΛCDM by ∼ 40%. Differences, therefore, are small but, however, DE does not ease the problem with cuspy DM profiles. On the contrary it could ease the discrepancy between ACDM and strong lensing data (Bertelmann 1998, 2002). We study also subhalos and find that, at z=0, the number of satellites coincides in all DE models. At higher z, DE models show increasing differences from ΛCDM and among themselves; this is the obvious pattern to distinguish between different DE state equations.