Neutron spectra have been measured for pure water and for boric acid solutions using the time-of-flight technique. After a critical review of the available calculational methods, three methods were selected for comparison with the experiments. The best method proved to be a transport code (modified DTF-IV) incorporating a bound hydrogen model based on the modified Haywood II frequency spectrum. For the pure-water spectrum, the largest discrepancy between theory and measurement was 16%.