  We study a nonlinear transport equation defined on an oriented network where
the velocity field depends not only on the state variable, but also on the
solution itself. We prove existence, uniqueness and continuous dependence
results for the solution of the problem intended in a suitable
measure-theoretic sense. We also provide a representation formula in terms of
the push-forward of the initial and boundary data along the network and discuss
an example of nonlocal velocity field fitting our framework.
