  We extend our Skyrme-Hartree-Fock (SHF) approach, which was used earlier to
describe successfully the single-$\Lambda$ hypernuclei, to investigate the
binding and the $\Lambda \Lambda$ bond energies of the double-$\Lambda$
hypernuclei. The nucleon-nucleon ($NN$) and $\Lambda$-nucleon ($\Lambda N$)
interactions are taken from our previous study. For the $\Lambda \Lambda$ force
several Skyrme-like potentials available in the literature have been used. We
discuss the sensitivity of the calculated $\Lambda \Lambda$ binding and bond
energies to the $\Lambda \Lambda$ and $\Lambda N$ force parameters. It is found
that the existing $\Lambda \Lambda$ hypernuclear data do not allow to
distinguish between various $\Lambda \Lambda$ force parameter sets used by us.
However, they show some selectivity for a particular set of the $\Lambda N$
potential determined in our previous work.
