  We consider the hyperfine structure, the atomic spectrum and the decay
channels of the bound mu+ mu- system (dimuonium). The annihilation lifetimes of
low-lying atomic states of the system lie in the nanosecond range range. The
decay rates could be measured by detection of the decay products (high energy
photons or electron-positron pairs). The hyperfine structure splitting of the
dimuonic system and its decay rate are influenced by electronic vacuum
polarization effects in the far time-like asymptotic region. This constitutes a
previously unexplored kinematic regime. We evaluate next--to-leading order
radiative corrections to the decay rate of low-lying atomic states. We also
obtain order alpha^5 corrections to the hyperfine splitting of the 1S and 2S
levels.
