Neutron-scattering experiments on (VO)(2)P2O7 reveal both a gapped magnon d
ispersion and an unexpected, low-lying second mode. The proximity and inten
sity of these modes suggest a frustrated coupling between the alternating s
pin chains. We deduce the minimal model containing such a frustration, and
show that it gives an excellent account of the magnon dispersion, static su
sceptibility, and electron-spin resonance absorption. We consider two-magno
n states which bind due to frustration, and demonstrate that these may prov
ide a consistent explanation for the second mode.