  From the fact that the nonperturbative self-energy contribution $C_{\rm SE}$
to the heavy meson mass is small: $C_{\rm SE}(b\bar{b})=0$; $C_{\rm
SE}(c\bar{c})\cong -40$ MeV \cite{ref.01}, strong restrictions on the pole
masses $m_b$ and $m_c$ are obtained. The analysis of the $b\bar{b}$ and the
$c\bar{c}$ spectra with the use of relativistic (string) Hamiltonian gives
$m_b$(2-loop)$=4.78\pm 0.05$ GeV and $m_c$(2-loop)$=1.39 \pm 0.06$ GeV which
correspond to the $\bar{\rm MS}$ running mass $\bar{m}_b(\bar{m}_b)=4.19\pm
0.04$ GeV and $\bar{m}_c(\bar{m}_c)=1.10\pm 0.05$ GeV. The masses $\omega_c$
and $\omega_b$, which define the heavy quarkonia spin structure, are shown to
be by $\sim 200$ MeV larger than the pole ones.
