In this manuscript rst we dene the notion of weak implicative hyper BCK -ideal of a hyper BCK -algebra. Then we state and prove some theorems which determine the relationship among this notion and (weak, commutative, (strong) implicative) hyper BCK -ideals, positive implicative hyper BCK -ideals of type 1, 3, . . . , 8 and (strong) pos- itive implicative hyper BCK -ideals. Specially, we prove that if H = {0, a, b, c} is a hyper BCK -algebra of order 4, such that a ◦ x = {0}, for all 0 = x ∈ H and I is a hyper BCK -ideal and weak implicative hyper BCK -ideal of H , then I is a positive implicative hyper BCK -ideal of type 3.