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We continue studying $6D, {\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM)theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. Using thesuperfield background field method we explore the two-loop divergencies of theeffective action in the gauge multiplet sector. It is explicitly demonstratedthat among four two-loop background-field dependent supergraphs contributing tothe effective action, only one diverges off shell. It is also shown that thedivergences are proportional to the superfield classical equations of motionand hence vanish on shell. Besides, we have analyzed a possible structure ofthe two-loop divergences on general gauge and hypermultiplet background.

On the two-loop divergences in 6D, ${\cal N}=(1,1)$ SYM theory