We present a general physical picture for the one-dimensional nanomagnetism of elements with only s- or sp-valence electrons based on the atomic orbital interactions, first-principles calculations and Stoner criterion combined. It is shown that s- and sp-electron atoms, such as Na, Mg, Al, and Si, can exhibit magnetism in the geometry of linear chains. The s- electron elements show magnetism when the bonds are compressed, and, in contrast, the sp-elements exhibit magnetism when the bonds are elongated. The underlying mechanism has been understood by a general physical picture, that is, the exchanges among electronic states of multiple subbands around the Fermi level. (C) 2009 Elsevier B. V. All rights reserved.