  Properties of some few-body systems which include one positively charged muon
$\mu^{+}$ and two electrons $e^{-}$ are discussed. In particular, we consider
the negatively charged muonium ion Mu$^{-}$ (or $\mu^{+} e^{-}_{2}$) and
four-body MuPs (or $\mu^{+} e^{-}_{2} e^{+}$) systems each of which has only
one stable bound (ground) state. The problem of annihilation of the
electron-positron pair(s) in the MuPs system is investigated. The hyperfine
structure splitting of the ground state in the MuPs system evaluated with our
expectation value of the muon-positron delta-function is $\Delta \approx$
23.05758 $MHz$. Another group of interesting four-body neutral systems
investigated in this study includes the $p^{+} \mu^{+} e^{-}_2, d^{+} \mu^{+}
e^{-}_2$ and $t^{+} \mu^{+} e^{-}_2$ `quasi-molecules'. These quasi-molecules
are formed in large numbers when positively charged muons slow down in liquid
hydrogen, or in liquid deuterium and/or tritium. The properties of these
systems are unique, since they occupy an intermediate position between actual
two-center molecules and one-center atoms.
