Due to an increasing problem of drug resistance among almost all parasites species ranging from protists to worms, there is an urgent need to explore new drug targets and their inhibitors to provide new and effective parasitic therapeutics. In this regard, there is growing interest in exploring known drug leads of human epigenetic enzymes as potential starting points to develop novel treatments for parasitic diseases. This approach of repurposing (starting with validated targets and inhibitors) is quite attractive since it has the potential to reduce the expense of drug development and accelerate the process of developing novel drug candidates for parasite control. Lysine deacetylases (KDACs) are among the most studied epigenetic drug targets of humans, and a broad range of small-molecule inhibitors for these enzymes have been reported. In this work, we identify the KDAC protein families in representative species across important classes of parasites, screen a compound library of 23 hydroxamate- or benzamide-based small molecules KDAC inhibitors, and report their activities against a range of parasitic species, including the pathogen of malaria (Plasmodium falciparum), kinetoplastids (Trypanosoma brucei and Leishmania donovani), and nematodes (Brugia malayi, Dirofilaria immitis and Haemonchus contortus). Compound activity against parasites is compared to that observed against the mammalian cell line (L929 mouse fibroblast) in order to determine potential parasite-versus-host selectivity). The compounds showed nanomolar to sub-nanomolar potency against various parasites, and some selectivity was observed within the small panel of compounds tested. The possible binding modes of the active compounds at the different protein target sites within different species were explored by docking to homology models to help guide the discovery of more selective, parasite-specific inhibitors. This current work supports previous studies that explored the use of KDAC inhibitors in targeting Plasmodium to develop new anti-malarial treatments, and also pioneers experiments with these KDAC inhibitors as potential new anthelminthics. The selectivity observed begins to address the challenges of targeting specific parasitic diseases while limiting host toxicity.