I will consider models solvable by the nested algebraic Bethe ansatz with gl(n)-invariant R-matrix (n$>$2). I also will consider their generalization to the superalgebras gl(m$mid$n). In distinction of the simplest gl(2) case, Bethe vectors in these models have a very non-trivial structure. Furthermore, calculating the scalar products of Bethe vectors is a very complex problem. I will explain how one can solve this problem. Several particular examples will be given for the algebras gl(3), gl(4), gl(2$mid$1), and gl(2$mid$2).