  Neutron-scattering experiments on (VO)_2P_2O_7 reveal both a gapped magnon
dispersion and an unexpected, low-lying second mode. The proximity and
intensity of these modes suggest a frustrated coupling between the alternating
spin chains. We deduce the minimal model containing such a frustration, and
show that it gives an excellent account of the magnon dispersion, static
susceptibility and electron spin resonance absorption. We consider two-magnon
states which bind due to frustration, and demonstrate that these may provide a
consistent explanation for the second mode.
