  We study dispersion relations in the noncommutative \phi^3 and Wess-Zumino
model in the Yang-Feldman formalism at one-loop order. Nonplanar graphs lead to
a distortion of the dispersion relation. We find that the strength of this
effect is moderate if the scale of noncommutativity is identified with the
Planck scale and parameters typical for a Higgs field are employed. The
contribution of the nonplanar graphs is calculated rigorously using the
framework of oscillatory integrals.
