  Using the hierarchy of scales between the mass, $M$, and the width, $\Gamma$,
of a heavy, unstable particle we construct an effective theory that allows
calculations for resonant processes to be systematically expanded in powers of
the coupling $\alpha$ and $\Gamma/M$. We illustrate the method by computing the
next-to-leading order line shape of a scalar resonance in an abelian
gauge-Yukawa model.
