The warble songs of budgerigars (Melopsittacus undulatus) are composed of a number of complex, variable acoustic elements that are sung by male birds in intimate courtship contexts for periods lasting up to several minutes. If these variable acoustic elements can be assigned to distinct acoustic-perceptual categories, it provides the opportunity to explore whether birds are perceptually sensitive to the proportion or sequential combination of warble elements belonging to different categories. By the inspection of spectrograms and by listening to recordings, humans assigned the acoustic elements in budgerigar warble from several birds to eight broad, overlapping categories. A neural-network program was developed and trained on these warble elements to simulate human categorization. The classification reliability between human raters and between human raters and the neural network classifier was better than 80% both within and across birds. Using operant conditioning and a psychophysical task, budgerigars were tested on large sets of these elements from different acoustic categories and different individuals. The birds consistently showed high discriminability for pairs of warble elements drawn from between acoustic categories and low discriminability for pairs drawn from within acoustic categories. With warble elements reliably assigned to different acoustic categories by humans and birds, it affords the opportunity to ask questions about the ordering of elements in natural warble streams and the perceptual significance of this ordering.