The present invention relates to an immunosuppressing method which comprises administering a spergualin-related compound represented by the following formula STR1 (wherein R1 is --(CH2)4 --, --(CH2)6 --, STR2 R2 is --(CH2)2 -- or --CH=CH--; and R3 is STR3 or pharmacologically acceptable salts thereof in an effective amount to a warm-blood animal.