RNA viruses are known to give rise to endogenous viral elements (EVEs) in the genomes of their hosts. This phenomenon is well-known amongst retroviruses, but it is relatively under-studied for RNA viruses and comparatively few endogenous RNA viral EVEs are known.  Using a HMM-based screening approach to target publicly available sequencing data, we have identified EVEs derived from the RdRp gene of members of the Nyamiviridae family of negative-strand RNA viruses in over 1,000 species of Lepidopteran insects (butterflies and moths). These insertions represent degraded viral RdRps. While viruses in this family are known to infect Lepidoptera, they have not previously been shown to have been endogenised in these hosts.  These EVEs form a large and diverse group throughout this insect order and appear to have been endogenised on multiple independent occasions. Related but distinct Nyamiviridae EVEs were also identified in other insect orders, such as bees and wasps (Hymenoptera), beetles (Coleoptera) and bugs (Hemiptera). Unexpectedly, in a number of cases, repeated copies of the RdRp-like region were found to occur consecutively within a small region of the host genome. These tandem repeats are present in over 20 diverse species of Lepidoptera, with at least four and up to 32 adjacent copies identified. To our knowledge, EVEs have not previously been known to display this tendency to occur as tandem repeats. The mechanism behind this phenomenon is not yet known, but may represent a novel route through which host species can build defences against RNA viral pathogens.