  This paper consists of two parts. In the first part we prove the unique
solvability for the abstract variational-hemivariational inequality with
history-dependent operator. The proof is based on the existing result for the
static variational-hemivariational inequality and a fixed point argument. In
the second part, we consider a mathematical model which describes quasistatic
frictional contact between a deformable body and a rigid foundation. In the
model the material behaviour is modelled by an elastic-viscoplastic
constitutive law. The contact is described with a normal damped response,
unilateral constraint and memory term. In the analysis of this model we use the
abstract result from the first part of the paper.
