Precise calculation of hyperfine structure of P -states in muonic ions of lithium, beryllium and boron in quantum electrodynamics is performed. We calculate
different corrections of orders alfa5 and alfa6 due to the vacuum polarization, nuclear structure and recoil in first and second orders of perturbation theory. 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 ions is used. The obtained values of hyperfine splittings can be used for a comparison with future experimental data.The work is supported by the RSF (Grant 18-12-00128)
