Suppose that? (X1, Z1),L,(Xn,Zn)? are independently and identically distributed bivariate random variables from parent (X,Z)?. Let Zn1,Zn2,L,Znn denote the induced order statistics and Mk(n) = max {Zn1+Zn2,……,Znk}. Based on the results of Gangopadhyay (1995), the almost sure limit theorem of the maximum Mk(n) is derived.