A sequence of nonnegative integers s=(S1, s2, , sn) is a score sequence of an r-tournament if, for some positive integer r, ther is a directed graph with vertices v1, v2, , vn such that deg+(vj)=sj and deg-(vj)=r(n-1) -sj for each j=1, 2, , n. The score sequence problem of an r-tournament is: Given some positive integer r and a sequence of nonnegative integers, determine whether it is a score sequence of an r-tournament or not. In this paper, we consider several variations of the score sequence problem of an r-tournament, and give efficient algorithms.