  We study quantum integrable models solvable by the nested algebraic Bethe
ansatz and possessing $\mathfrak{gl}(m|n)$-invariant $R$-matrix. We compute the
norm of the Hamiltonian eigenstates. Using the notion of a generalized model we
show that the square of the norm obeys a number of properties that uniquely fix
it. We also show that a Jacobian of the system of Bethe equations obeys the
same properties. In this way we prove a generalized Gaudin hypothesis for the
norm of the Hamiltonian eigenstates.
