  Focusing on a string-hole gas within the pre-big bang scenario, we study the
stability of its solutions in the phase space. We firstly extend the analysis
present in the literature relaxing the ideal-gas properties of the string-hole
gas, taking into account a (bulk-)viscosity term. Then we consider the case of
a theory described by a complete O(d,d)-invariant action up to all orders in
$\alpha^{\prime}$-corrections (the Hohm-Zwiebach action), studying the
stability of the string-hole gas solution with or without the introduction of
the viscosity term. Furthermore, the bulk viscosity is also considered for two
different first order $\alpha^{\prime}$-corrected actions: the
Gasperini-Maggiore-Veneziano-action and the Meissner-action. The results
obtained show how the viscosity can help to stabilize the string-hole gas
solution, obtaining constraints on the equation of state of the gas.
