  The shear ($\eta$) and bulk ($\zeta$) viscosities are calculated in a
quasiparticle relaxation time approximation. The hadron phase is described
within the relativistic mean field based model with scaled hadron masses and
couplings. The quark phase is treated in terms of the heavy quark bag model
fitted to the lattice data. A two-phase model allowing for the first order
phase transition from the hadron phase to the strongly coupled quark gluon
plasma is constructed by means of the Gibbs conditions. Temperature and baryon
density dependence of the calculated viscosity-to-entropy ratios ($\eta/s$,
$\zeta/s$) are analyzed and compared with those obtained in other models.
Special attention is paid to the behavior of viscosity coefficients near the
critical temperature, from both hadron and quark-gluon side. Effects of
resonance widths on viscosities and viscosity-to-entropy ratios are estimated.
