Co-59 NMR relaxation rates were measured for the Delta-[Co(R,R-chxn)(3)](3+) (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-1 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-1 relaxation rates increased with increasing anion concentrations. An analysis of the concentration dependences of the Co-59 and H-1 relaxation rates, assuming 1:1 and 1:2 ion pairs between the metal complex ion and the anion, indicates a substantial decrease in the Co-59 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 Co-59 relaxation rates for [Co(chxn)(3)](3+) can be attributed to the difference in the lifetime of the configuration of their 1:1 ion pairs. .?z