  In this paper the expected properties of the velocity fields of strongly
lensed arcs behind galaxy clusters are investigated. The velocity profile along
typical lensed arcs is determined by ray tracing light rays from a model source
galaxy through parametric cluster toy-models consisting of individual galaxies
embedded in a dark cluster halo. We find that strongly lensed arcs of high
redshift galaxies show complex velocity structures that are sensitive to the
details of the mass distribution within the cluster, in particular at small
scales. From fits to the simulated imaging and kinematic data we demonstrate
that reconstruction of the source velocity field is in principle feasible: two
dimensional kinematic information obtained with Integral Field Units (IFU's) on
large ground based telescopes in combination with adaptive optics will allow
the reconstruction of rotation curves of lensed high redshift galaxies. This
makes it possible to determine the mass-to-light ratios of galaxies at
redshifts z>1 out to about 2-3 scale lengths with better than about 20%
accuracy. We also discuss the possibilities of using two dimensional kinematic
information along the arcs to give additional constraints on the cluster lens
mass models.
