Deconfinement of Constituent Quarks and the Hagedorn Temperature
  The double phase transition of hadronic matter, $H$, first, to the gas of deconfined constituent quarks (for brevity called {\it valons}), $Q$, and then, secondly, the phase transition from $Q$ to quark-gluon plasma, $QGP$, is considered within bag model ideology. In distinction from previous double phase transition investigations, it is not supposed that at zero chemical potential (~$\mu=0$~) transition temperatures $T_d$ (for $H~\leftrightarrow~Q$) and $T_{ch}$ (for $Q~\leftrightarrow~ QGP$, chiral restoration) coincide. Then for plausible range of chosen bag constants, $B_Q$ for $Q$ and $B_q$ for $QGP$ the phase transition $H~ \leftrightarrow~ QGP$ can proceed {\it only via the $Q$ phase} (at least at not too much $\mu$). For small $\mu$ the gap, $T_{ch}~-~T_d$, is quite essential, up to $\approx~50$ MeV. The physical meaning of the $H~ \leftrightarrow~ Q$ transition temperature, $T_d$, coincide with that of the Hagedorn temperature, $T_H$. 
O.D. Chernavskaya, E.L. Feinberg (P.N.Lebedev Physical Institute,   Russia)