  Recent experiments on the laser-induced resonant annihilation provide a
precise measurement of transition energies of antiprotonic helium atoms.
Relativistic corrections of an order of $\alpha ^2$ to the pure Coulomb
interaction will be taken into account in the theoretical description of energy
spectra of antiprotonic helium atoms. The splitting of energy levels arising
due to the spin-dependent part of the relativistic interaction is considered
for a number of states of $^{3,4}\! H\! e\bar pe$ systems.
