In the study of quasiperiodically forced systems invariant graphs have a special significance. In some cases, it was already possible to deduce statements about the invariant graphs of certain classes of systems from properties of the fibre maps. Here, we study quasiperiodically forced interval maps which are monotonically increasing and have negative Schwarzian derivative. First, we derive some basic results which only require monotonicity. Then we give a classification, with respect to the number and to the Lyapunov exponents of invariant graphs, for this class of systems. It turns out that the possibilities for the invariant graphs are exactly analogous to those for the fixed points of the unperturbed fibre maps.