The calculations of the energies of the singlet doubly excited states 2p 2 1 D, 3d 2 1 G, 4f 2 1 I of helium-like systems we have done in our previous paper [Biaye et al., Eur. Phys. J. D 13, 21 (2001).] are extended to the other singlet doubly excited (nl) 2 states with n ≤ 4. The energies are calculated in the framwork of the variation method by using some special forms of Hylleraasa-type wave functions with a real Hamiltonian. The results which we have obtained are in good agreement with some experimental data and other theoretical results.