  Stability of the bound ground states in the six five-body muonic $a b \mu
e_2$ ions (or $(a b \mu e_2)^{-}$) and ten six-body $a b c \mu e_2$
quasi-molecules is investigated. The notations $a, b, c$ stand for the bare
nuclei of three hydrogen isotopes - protium ($p$), deuterium ($d$) and tritium
($t$). All these systems are the Coulomb five- and six-body systems with unit
charges. It is found that the ground bound $S(L = 0)-$states are stable in all
six five-body $a b \mu e_2$ ions and in ten six-body $a b c \mu e_2$
quasi-molecules. As follows from accurate variational computations of the
five-body $a b \mu e_2$ ions their internal structure is similar to the
internal structure of the negatively charged hydrogen ion H$^{-}$. Analogously,
we show that the internal structures of the six-body neutral $a b c \mu e_2$
quasi-molecules are similar to the structure of the two-center H$_{2}$ molecule
which contains two heavy hydrogen nuclei and two bound electrons.
