Let G be an abelian group with identity e. Let R be a graded multiplicative hyperring and δ : I r (R) → I r (R) be an expansion function of I r (R), where I r (R) is the set of all graded hyperideals of R. In this paper, we introduce and study the concepts of graded δ-primary hyperideals of R and graded 2-absorbing δ-primary hyperideals of R which are the extended classes of graded prime and graded 2-absorbing hyperideals of R, respectively. Moreover, we give the basic properties of these new types of graded hyperideals and investigate the relations among these structures