  The nonextensive one-dimensional version of a hydrodynamical model for
multiparticle production processes is proposed and discussed. It is based on
nonextensive statistics assumed in the form proposed by Tsallis and
characterized by a nonextensivity parameter $q$. In this formulation the
parameter $q$ characterizes some specific form of local equilibrium which is
characteristic for the nonextensive thermodynamics and which replaces the usual
local thermal equilibrium assumption of the usual hydrodynamical models. We
argue that there is correspondence between the perfect nonextensive
hydrodynamics and the usual dissipative hydrodynamics. It leads to simple
expression for dissipative entropy current and allows for predictions for the
ratio of bulk and shear viscosities to entropy density, $\zeta/s$ and $\eta/s$,
to be made.
