Whereas most of crystalline Al(Si)-Mn and Al(Si)-Pd-Mn phases are non-magnetic, measurements show the existence of localized magnetic moments on a small fraction of the Mn atoms in quasicrystals and in a few crystalline approximants. We develop a new model that shows that an indirect Mn-Mn interaction via the conduction band is determinant for the existence or not of a magnetic moment, even when Mn-Mn distance is 5A or more. These models allow us to understand experimental measurements. © 2001 Elsevier Science B.V. All rights reserved.