  A transport theory is developed on the quark level to describe
nucleon--nucleon collisions. We treat the strong interaction effectively by the
Friedberg-Lee model both in its original and in its modified confining version.
First we study the stability of the static three-dimensional semiclassical
configuration, then we present results of the time evolution given by a Vlasov
equation for the quarks coupled to a Klein-Gordon equation for the mean field.
We find at higher energies that the nucleons are almost transparent, whereas at
lower energies we observe a substantial interaction. At very low energies we
see a fusion of our bags, which is due to the purely attractive nature of the
mean field and hence is an artifact of our model. We test the confinement
mechanism and find that at higher energies the nucleons are restored shortly
after the collision.
