This paper is the first part of a three (3) part series of reviews that serves to shed light on the parasites which inhabit the gastrointestinal tract of domestic animals imported into the New World tropics (Neo-tropics), the domesticated Neo-tropical animals and the non-domesticated Neo-tropical animals (wildlife). This first review has focused on the domesticated animals introduced into the new world tropics (Neo-tropics) which were brought by the early European settlers four to five hundred years ago. These introduced Old World domesticated animal species were cattle (Bos taurus, B. indicus), sheep (Ovis aries), goat (Capra hircus), pigs (Sus scrofa), horses (Equus caballus) and chicken (Gallus domestiucus). The references used in this review were gathered and synthesized to give a clear breakdown of gastrointestinal parasites of Old World Domesticated animals. The references spanned sixty five (65) years, the earliest reference cited was in 1953 and the most recent was 2018. Most classes of gastrointestinal parasites were reviewed and tabulated by species; they were trematodes, nematodes, cestodes and coccidian. Gastrointestinal parasites which have been reported in domestic livestock species, have negatively affected the health and performances of the animals. The drugs used have been tabulated across animal species.