An ion beam resonates with R‐mode waves at two frequency bands. These are a high frequency RH mode (ω » Ωp) and a low frequency RL mode (ω ∼ ΩH2O+), where Ωpand ΩH2O+are cyclotron frequencies of protons and water ions, respectively. We study the nonlinear evolution of beam‐generated RH waves by one‐dimensional hybrid computer experiments. Both wave‐particle and subsequent wave‐;wave interactions are examined. We find that the RH waves through the interaction with an ion beam formed by pick‐up heavy ions near comets, grow to a level ofBw/Bo∼ 0.23. The waves saturate by wave‐wave interactions (via the decay instability) supplying energy to backward travelling daughter R‐mode waves with slightly lowerk(and hence lower ω) as well as forward travelling longitudinal waves. The backward travelling daughter R‐mode waves decay further to granddaughter waves with still lowerk. We show that this inverse cascading process occurs faster than the growth of the RL mode instability and produces a wide band wave spectrum which extends from the wavenumber of beam‐excited RH mode to much lowerk. The nonlinearly excited longitudinal sound waves play a rol