- We study the gas distribution in the Milky Way and Andromeda using a constrained cosmological simulation of the Local Group (LG) within the context of the CLUES (Constrained Local UniversE Simulations) project. We analyse the properties of gas in the simulated galaxies at z = 0 for three different phases: 'cold', 'hot' and H i, and compare our results with observations. The amount of material in the hot halo (M-hot a parts per thousand 4-5 x 10(10) M-aS (TM)), and the cold (M-cold(r a parts per thousand(2) 10 kpc) a parts per thousand 10(8) M-aS (TM)) and H i components displays reasonable agreement with observations. We also compute the accretion/ejection rates together with the H i (radial and all-sky) covering fractions. The integrated H i accretion rate within r = 50 kpc gives similar to 0.2-0.3 M-aS (TM) yr(-1), i.e. close to that obtained from high-velocity clouds in the Milky Way. We find that the global accretion rate is dominated by hot material, although ionized gas with T a parts per thousand(2) 10(5) K can contributeWe study the gas distribution in the Milky Way and Andromeda using a constrained cosmological simulation of the Local Group (LG) within the context of the CLUES (Constrained Local UniversE Simulations) project. We analyse the properties of gas in the simulated galaxies at z = 0 for three different phases: 'cold', 'hot' and H i, and compare our results with observations. The amount of material in the hot halo (M-hot a parts per thousand 4-5 x 10(10) M-aS (TM)), and the cold (M-cold(r a parts per thousand(2) 10 kpc) a parts per thousand 10(8) M-aS (TM)) and H i components displays reasonable agreement with observations. We also compute the accretion/ejection rates together with the H i (radial and all-sky) covering fractions. The integrated H i accretion rate within r = 50 kpc gives similar to 0.2-0.3 M-aS (TM) yr(-1), i.e. close to that obtained from high-velocity clouds in the Milky Way. We find that the global accretion rate is dominated by hot material, although ionized gas with T a parts per thousand(2) 10(5) K can contribute significantly too. The net accretion rates of all material at the virial radii are 6-8 M-aS (TM) yr(-1). At z = 0, we find a significant gas excess between the two galaxies, as compared to any other direction, resulting from the overlap of their gaseous haloes. In our simulation, the gas excess first occurs at z similar to 1, as a result of the kinematical evolution of the LG.…