  Spectral stability of multi-hump vector solitons in the Hamiltonian system of
coupled nonlinear Schr\"{o}dinger (NLS) equations is investigated both
analytically and numerically. Using the closure theorem for the negative index
of the linearized Hamiltonian, we classify all possible bifurcations of
unstable eigenvalues in the systems of coupled NLS equations with cubic and
saturable nonlinearities. We also determine the eigenvalue spectrum numerically
by the shooting method. In case of cubic nonlinearities, all multi-hump vector
solitons in the non-integrable model are found to be linearly unstable. In case
of saturable nonlinearities, stable multi-hump vector solitons are found in
certain parameter regions, and some errors in the literature are corrected.
