In a group of transition metal complexes that scientists have synthesized to find a good replacement for cisplatin, ruthenium complexes, with various good properties, occupy a very important place. In this group, ruthenium polypyridyl complexes showed promising properties and became leading candidates for use as anticancer agents. In this study, we have synthesized a new ruthenium (II) polypyridyl complex of general formula [Ru(L)(N-N)Cl]Cl, where L is 2,2’:6’,2’’-terpyridine with the additional functional group in the 4’-position: 2-thienly and N-N= bpy (2,2’-bypiridine). The kinetics of the substitution reactions of the studied complex with important biomolecules, the nitrogen-containing ligand 5’-GMP and the S-containing ligand LCys, were monitored. The kinetic results showed a faster substitution of the labile aqua ligand with a nitrogen-containing ligand, than a sulfur-containing one.