The behavior near the singularity of an isotropic, homogeneous cosmolo
gical model with a viscous fluid source is investigated. This turns ou
t to be a relaxation dominated regime. Full extended irreversible ther
modynamics is used, and a comparison with results of the truncated the
ory is made. New singular behaviors are found and it is shown that a r
elaxation dominated inflationary epoch may exist for fluids with a sma
ll heat capacity.