  Energies of the low-lying bound S-states (L=0) of exotic three-body systems,
consisting a nuclear core of charge +Ze (Z being atomic number of the core) and
two negatively charged valence muons, have been calculated by hyperspherical
harmonics expansion method (HHEM). The three-body Schr\H{o}dinger equation is
solved assuming purely Coulomb interaction among the binary pairs of the
three-body systems X$^{Z+}\mu^-\mu^-$ for Z=1 to 54. Convergence pattern of the
energies have been checked with respect to the increasing number of partial
waves $\Lambda_{max}$. For available computer facilities, calculations are
feasible up to $\Lambda_{max}=28$ partial waves, however, calculation for still
higher partial waves have been achieved through an appropriate extrapolation
scheme. The dependence of bound state energies has been checked against
increasing nuclear charge Z and finally, the calculated energies have been
compared with the ones of the literature.
