The diversification of neoavian birds is one of the most rapid adaptive radiations of extant organisms. Recent whole-genome sequence analyses have much improved the resolution of the neoavian radiation and suggest concurrence with the Cretaceous-Paleogene (K-Pg) boundary, yet the causes of the remaining genome-level irresolvabilities appear unclear. Here we show that genome-level analyses of 2,118 retrotransposon presence/absence markers converge at a largely consistent Neoaves phylogeny and detect a highly differential temporal prevalence of incomplete lineage sorting (ILS), i.e., the persistence of ancestral genetic variation as polymorphisms during speciation events. We found that ILS-derived incongruences are spread over the genome and involve 35% and 34% of the analyzed loci on the autosomes and the Z chromosome, respectively. Surprisingly, Neoaves diversification comprises three adaptive radiations, an initial near-K-Pg super-radiation with highly discordant phylogenetic signals from near-simultaneous speciation events, followed by two post-K-Pg radiations of core landbirds and core waterbirds with much less pronounced ILS. We provide evidence that, given the extreme level of up to 100% ILS per branch in super-radiations, particularly rapid speciation events may neither resemble a fully bifurcating tree nor are they resolvable as such. As a consequence, their complex demographic history is more accurately represented as local networks within a species tree.