  For $6D$, ${\cal N}=(1,1)$ SYM theory formulated in ${\cal N}=(1,0)$ harmonic
superspace as a theory of interacting gauge multiplet and hypermultiplet we
construct the ${\cal N}=(1,1)$ supersymmetric Heisenberg-Euler-type superfield
effective action. The effective action is computed for the slowly varying
on-shell background fields and involves, in the bosonic sector, all powers of a
constant abelian strength.
