We develop a theory of impact of viscoelastic spheres with adhesive
interactions. We assume that the collision velocities are not large to
avoid the fracture and plastic deformation of particles material and
microscopic relaxation time is much smaller than the collision duration.
The adhesive interactions are described with the use of Johnson, Kendall
and Roberts (JKR) theory, while dissipation is attributed to the
viscoelastic behavior of the material. For small impact velocities we
apply the condition of a quasi-static collision and obtain the
inter-particle force. We show that this force is a sum of four
components, having in addition to common elastic, viscous and adhesive
force, the visco-adhesive cross term. Using the derived force we compute
the coefficient of normal restitution and consider the application of our
theory to the collisions of macro and nano-particles.