Krasner F (m,n) -hyperrings were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three particular classes of F -hyperideals in a Krasner F (m,n) -hyperring, namely prime F -hyperideals, maximal F -hyperideals and primary F -hyperideals, which extend similar concepts of ring context. Furthermore, we examine the relations between these structures. Then a number of major conclusions are given to explain the general framework of these structures.Key words and phrases. prime F -hyperideal, maximal F -hyperideal, primary F -hyperideal, Krasner F (m,n) -hyperring. * ) be the set of all fuzzy subsets of G.the following conditions are satisfied: (1) (a•b)•c = a•(b•c) for all a, b, c ∈ G, (2) there exists e ∈ G with a ∈ supp(a•e∩e•a), for all a ∈ G, (3) for each a ∈ G, there exists a unique element afor all a, b, c ∈ G. Indeed, a fuzzy hyperoperation assigns to each pair of elements of G a non-zero fuzzy subset of G, while a hyperoperation assigns to each pair of elements of G a non-empty subset of G. The concepts of Krasner F (m,n) -hyperrings and F -hyperideals were defined in [14] by Farshi and Davvaz. In this paper, we continue the study of F -hyperideals of a Krasner F (m,n) -hyperring, initiated in [14]. We define and analyze there particular types of F -hyperideals in a Krasner F (m,n) -hyperring, maximal F -hyperideals and primary F -hyperideals. We investigate the connections between them. Moreover, we introduce the concepts of F -radical, quotient Krasner F (m,n) -hyperring and Jacobson radical. The overall framework of these structures is then explained. It is shown (Theorem 4.6) that if Q is an primary F -hyperideal of a Krasner F (m,n)hyperring (R, f, g), then √ Q F is a prime F -hyperideal of R. PreliminariesIn this section we recall some basic terms and definitions from [14] which we need to develop our paper.