We calculate the expected finite frequency neutron scattering intensity based on the two-sublattice collinear antiferromagnet found by recent neutron scattering experiments as well as by theoretical analysis on the iron oxypnictide LaOFeAs. We consider two types of superexchange couplings between Fe atoms: nearest-neighbor coupling J1 and next-nearest-neighbor coupling J2. We show how to distinguish experimentally between ferromagnetic and antiferromagnetic J1. Whereas magnetic excitations in the cuprates display a so-called resonance peak at (pi,pi) (corresponding to a saddlepoint in the magnetic spectrum) which is at a wavevector that is at least close to nesting Fermi-surface-like structures, no such corresponding excitations exist in the iron pnictides. Rather, we find saddlepoints near (pi,pi/2) and (0,pi/2)(and symmetry related points). Unlike in the cuprates, none of these vectors are close to nesting the Fermi surfaces.
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