  We present an extension of the duality theorem, previously defined by S.
Catani et al. on the one-loop level, to higher loop orders. The duality theorem
provides a relation between loop integrals and tree-level phase-space
integrals. Here, the one-loop relation is rederived in a way which is more
suitable for its extension to higher loop orders. This is shown in detail by
considering the two-loop N-leg master diagram and by a short discussion of the
four master diagrams at three loops, in this sketching the general structure of
the duality theorem at even higher loop orders.
