59C0 NMR relaxation rates were measured for the A-[Co(R,R-chxn)3I3+ (chxn = trans-( 1R,2R)-1,2-diaminocyclohexane) in the presence of multivalent anions such as sulfate, hydrogen phosphate, phosphate, oxalate, and ethanedisulfonate. The relaxation rates decreased with an addition of sulfate, hydrogen phosphate, and phosphate ions below a concentration of 0.1 mol dm-3 and then increased above this concentration. On the other hand, with an addition of oxalate and ethanedisulfonate ions, the relaxation rates steadily increased.'H relaxation rates of the chxn ligands in the chxn complex were also measured in the presence of sulfate and oxalate ions. In both systems the 'H relaxation rates increased with increasing anion concentrations. An analysis of the concentration dependences of the 59C0 and 'H relaxation rates, assuming 1:l and 1:2 ion pairs between the metal complex ion and the anion, indicates a substantial decrease in the 59C0 electric field gradient by the formation of the 1: 1 ion pair with the sulfate ion. The difference between the sulfate and oxalate ions regarding their effects on the 59C0 relaxation rates for [Co(chxn)3l3+ can be attributed to the difference in the lifetime of the configuration of their 1:l ion pairs.