The Equidae (the horse, Equus caballus, the ass, Equus asinus, zebras and their hybrids) are hosts to a great variety of nematode parasites, some of which can cause significant morbidity or mortality if individual hosts are untreated. Worldwide the nematode parasites of horses belong to 7 suborders, 12 families, 29 genera and 83 species. The great majority (19 of 29 genera and 64 of 83 species) are members of the family Strongylidae, which includes the most common and pathogenic nematode parasites of horses. Only the Strongylidae are included in this treatise. The Strongylidae (common name strongylids) of horses--nematodes with a well-developed buccal capsule, a mouth collar with two leaf-crowns, and a strongyloid (common name of superfamily Strongyloidea) copulatory bursa--can be separated into two subfamilies: Strongylinae (common name strongylins), usually large or medium-sized with a globular or funnel-shaped buccal capsule; and Cyathostominae (common name cyathostomins), usually small to medium-sized with a cylindrical buccal capsule. The increased attention to strongylid nematode parasites of horses has resulted in the need for updated diagnostic keys to these parasites using readily recognizable characters and the most recent literature on their systematics. Because the cyathostomins have been historically difficult to identify, and because they have emerged as the most significant nematode pathogens of horses, we provide a brief nomenclatural and taxonomic history and an introduction to the morphology of this group. This treatise is intended to serve as a basic working tool--providing easy identifications to genus and species of adult strongylid nematodes of equids. All strongylid nematodes normally parasitic in horses, the ass (and their hybrids), and zebras are included. The keys are illustrated with line drawings and halftone photomicrographs of each species. A short discussion of the systematics of the genus and species is provided for each genus following the species descriptions. Species diagnoses and a synonymy of each species is provided. Geographic distribution, prevalence, and location in host are also given for each species.