ABSTRACT To study the local Hubble flow, we have run constrained dark matter (DM) simula-tions of the Local Group (LG) in the concordance ΛCDM and OCDM cosmologies,with identical cosmological parameters apart from the Λ term. The simulations wereperformed within a computational box of 64h −1 Mpc centred on the LG. The initialconditions were constrained by the observed peculiar velocities of galaxies and posi-tions of X-ray nearby clusters of galaxies. The simulations faithfully reproduce thenearby large scale structure, and in particular the Local Supercluster and the Virgocluster. LG-like objects have been selected from the DM halos so as to closely resemblethe dynamical properties of the LG. Both the ΛCDM and OCDM simulations showvery similar local Hubble flow around the LG-like objects. It follows that, contrary torecent statements, the dark energy (DE) does not manifest itself in the local dynamics.Key words: galaxies: Local Group – cosmology: dark matter – methods: N-bodysimulations