  We study perturbative amplitudes in a large class of theories obtained by
marginal deformations of the N=4 supersymmetric Yang-Mills. We find that planar
amplitudes in the deformed theories are closely related to planar amplitudes in
the original N=4 SYM. For some classes of deformations the amplitudes
essentially coincide with the N=4 amplitudes to all orders in planar
perturbation theory. For more general classes of marginal deformations, the
equivalence holds at up to four loops, and at five loops it is likely to break
down. This implies that the iterative structure of planar MHV amplitudes
recently discovered by Bern, Dixon and Smirnov in hep-th/0505205 for the N=4
theory also manifests itself in a wider class of theories.
