Rational normal curves contained in Segre varieties

Let X be any Segre variety. We give a complete description of the degrees of the smooth rational curves contained in X which are rational normal curves in their linear span. We give a partial description of the algebro-geometric properties of these rational curves, e.g. since X is a linearly normal embedding of a multiprojective space, their multidegree. There are forbidden multidegrees for these curves.