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Elaborated calculations of the shear and the bulk viscosities in the hadrongas, using the ultrarelativistic quantum molecular dynamics (UrQMD) model crosssections, are made. These cross sections are analyzed and improved. A specialtreatment of the resonances is implemented additionally. All this allows forbetter hydrodynamical description of the experimental data. The previouslyconsidered approximation of one constant cross section for all hadrons isjustified. It's found that the bulk viscosity of the hadron gas is much largerthan the bulk viscosity of the pion gas while the shear viscosity is found tobe less sensitive to the hadronic mass spectrum. The maximum of the bulkviscosity of the hadron gas is expected to be approximately in the temperaturerange ${T=150 190 MeV}$ with zero chemical potentials. This range covers thecritical temperature values found from lattice calculations. We comment on someimportant aspects of calculations of the bulk viscosity, which were not takeninto account or were not analyzed well previously. Doing this, a generalizedChapman-Enskog procedure, taking into account deviations from the chemicalequilibrium, is outlined. Some general properties, features, the physicalmeaning of the bulk viscosity and some other comments on the deviations fromthe chemical equilibrium supplement this discussion. Analytical closed-formexpressions for the transport coefficients and some related quantities within aquite large class of cross sections can be obtained. Some examples areexplicitly considered. Comparisons with some previous calculations of theviscosities in the hadron gas and the pion gas are done.

Analytical formulas, general properties and calculation of transport coefficients in the hadron gas: shear and bulk viscosities