  The formation of Ps in our Galaxy is well measured, and has led to important
and unanswered questions on the origin of the positrons. In principle it should
be possible to form analogous systems from mu and tau leptons, viz. true
muonium and true tauonium. However the probability of formation for these
systems is greatly reduced due to the intrinsically short lifetimes of the mu
and tau leptons. Likewise, the decay of the atoms is hastened by the high
probability of the constituent particles decaying. Nevertheless, if sufficient
numbers of mu and tau pairs are produced in high energy astrophysical
environments there may be significant production of true muonium and true
tauonium, despite the small probabilities. This paper addresses this
possibility.
  We have calculated the pair production spectra of mu and tau leptons from
photon-photon annihilation and electron-positron annihilation in astrophysical
environments. We have computed the cross-sections for radiative recombination
and direct annihilation of the pairs, and the decay constants for the various
allowable decays, and the wavelengths and energies of the recombination and
annihilation signatures. In this way we have calculated the probabilities for
the formation of true muonium and true tauonium, and the branching ratios for
the various observable signatures.
  We have estimated the expected fluxes from accretion discs around
microquasars and active galactic nuclei, and from interactions of jets with
clouds and stars. We find that accretion discs around stellar mass black holes
in our own Galaxy should have observable signatures at X-ray and gamma-ray
energies that are in principle observable with current observatories.
