Transition metal ions exhibit a unique role in diverse biological activities of proteins by acting as cofactors. In particular, zinc and copper ions modulate enzymes activities as well as many catalytic and oxidative/reductive processes. The kinetics and mechanism of the substitution reactions of dichloro [ZnCl₂(terpy)] and [CuCl₂(terpy)]  (terpy = 2,2′:6′,2′′-terpyridine) with biologically relevant ligands have been studied as a function of nucleophile concentrations at pH 7.38, under pseudo-first-order condition by UV-Vis spectrophotometric techniques. The interactions of Cu(II) and Zn(II) complexes with tripeptide glutathione (GSH) were investigated under pseudo-first-order conditions with respect to the complex concentration. For the substitution process of Zn(II) complex with glutathione (GSH), pre-equilibrium and chelate formation have been noted. The [CuCl₂(terpy)] is more reactive than [ZnCl₂(terpy)] complex and the second-order rate constants for the first step follow the order of reactivity: GSH > DL-Asp > L -Met > 5’-GMP ~ 5’-IMP for Cu(II)  complex,  while for Zn(II) the order of reactivity is: DL-Asp >  L -Met > GSH ~  5’-GMP > 5’-IMP. The results are discussed in terms of mechanisms of interactions between metalloproteins and biomolecules.