  The hyperfine structure splittings of the ground states of the $pd\mu, pt\mu$
and $dt\mu$ ions are determined with the use of highly accurate expectation
values of the interparticle delta-functions obtained in recent computations.
The corresponding hyperfine structure splittings, e.g., $\Delta_{12} =$
1.3400149$\cdot 10^7$ $MHz$ and $\Delta_{23} =$ 3.3518984$\cdot 10^7$ $MHz$ for
the $pt\mu$ ion, can directly be measured in modern experiments.
