Methods to elevate white blood cell counts in animal subjects using compounds of formula (1) are disclosed. These compounds have the formulaor pharmaceutically acceptable salt thereofwherein Z is a cyclic polyamine containing 9-32 ring members of which 3-8 are nitrogen atoms, said nitrogen atoms separated from each other by at least 2 carbon atoms, and wherein said heterocycle may optionally contain additional heteroatoms besides nitrogen and/or may be fused to an additional ring systemZ may be embodied in a form as defined by Z above, or alternatively may be of the formulawherein each R is independently H or straight, branched or cyclic alkyl (1-6C), n is 1 or 2, and X is an aromatic ring, including heteroaromatic rings, or is a mercaptan"linker" represents a bond, alkylene (1-6C) or may comprise aryl, fused aryl, oxygen atoms contained in an alkylene chain, or may contain keto groups or nitrogen or sulfur atomsin an amount effective to elevate said WBC count in said subject.