  On the basis of quasipotential approach to the bound state problem in quantum
electrodynamics we calculate hyperfine structure intervals Delta
E^{hfs}(2P_{1/2}) and Delta E^{hfs}(2P_{3/2}) for P-states in muonic deuterium.
The tensor method of projection operators for the calculation of the hyperfine
structure of P-states with definite quantum numbers of total atomic momentum F
and total muon momentum j in muonic deuterium is formulated. We take into
account vacuum polarization, relativistic, quadrupole and structure corrections
of orders alpha^4, alpha^5 and alpha^6. The obtained numerical values of
hyperfine splittings are useful for the analysis of new experimental data of
the CREMA collaboration regarding to muonic deuterium.
