Predictability in the composition of tropical assemblages of insect herbivores was studied using a sample of 35 952 caterpillars (Lepidoptera) from 534 species, feeding on 69 woody species from 45 genera and 23 families in a lowland rainforest in Papua New Guinea. Caterpillar assemblages were strongly dominated by a single species (median 48% of individuals and 49% of biomass). They were spatially and temporally constant (median normalized expected species shared (NESS) similarity between assemblages from the same host was greater than or equal to 0.85 for three sites 8–17 km apart as well as for three four–month periods of the year). Further, the median presence of species was 11 months per year. Assemblages on hosts from different families and genera were virtually disjunct (NESS similarity less than 0.05) as the caterpillars were mostly specialized to a single plant family (77% of species) and, within families, to a single genus (66% of species), while capable of feeding on multiple congeneric hosts (89% of species). The dominance of caterpillar assemblages by a small number of specialized species, which also exhibited low spatial and temporal variability, permitted robust and reliable estimates of assemblage composition and between–assemblage similarity from small samples, typically less than 300 individuals per host plant. By contrast, even considerably larger samples were insufficient for estimates of species richness. A sample of 300 individuals was typically obtained from 1050 m2 of foliage sampled during 596 tree inspections (i.e. a particular tree sampled at a particular time) in the course of 19 sampling days (median values from 69 assemblages). These results demonstrate that, contrary to some previous suggestions, insect herbivore assemblages in tropical rainforests have a predictable structure and, as such, are amenable to study.