Molecular dynamics simulations of the unliganded T state of human hemoglobin showed the existence of a spontaneous, very wide cavity on the distal side of the alpha subunit. This cavity consists of three tunnels spreading from the vicinity of the iron atom (the ligand binding site) to the surface of the subunit, constituting possible passageways for the entrance of the ligand. A fourth passageway was characterized due to the trajectory of water molecules entering or leaving the heme pocket. Analogous passages were observed in the beta subunits. They all appear and disappear dynamically, although some parts of them are more persistent along the trajectories. The most persistent regions within these tunnels correspond to all the xenon docking sites of human cytoglobin and to some of those of sperm whale and horse heart myoglobins and group I truncated hemoglobins.