Magnetic susceptibilities for adsorbed O-2 on heat-treated single-wall carbon nanohorns (HT-SWNHs) showed anomalous features as compared with those on as-grown SWNHs. Magnetism for the latter case was similar to that for bulky solid O-2, indicating the magnetic phase transitions associated with gaseous to liquid and in solid states (gamma-beta and beta-alpha). On the other hand. magnetism associated with gamma-beta transition was not observed for O-2, adsorbed on HT-SWNHs. For HT-SWNHs, O-2, can get into the interior of SWNH from the nano-windows, which were opened by heat-treatment, and solidify. We therefore concluded that the gamma-beta transition was suppressed in the nano-meter sized space. (C) 2004 Elsevier B.V. All rights reserved.