Eysyslopterus is classified as part of the family Adelophthalmidae, the only clade within the derived ("advanced") Adelophthalmoidea superfamily of eurypterids.

One fossil of the single and type species, E. patteni, has been discovered in deposits of the Late Silurian period (Ludlow epoch) in Saaremaa, Estonia.

The species name honors William Patten, an American biologist and zoologist who discovered the only known fossil of Eysyslopterus.

The total size of the only known specimen is estimated at only 8 centimetres (3.1 inches),[1] far from the largest adelophthalmids like Adelophthalmus khakassicus of 32 cm (12.6 in) in length.

[4] Eysyslopterus is only known from one single specimen (and is therefore the holotype, AMNH 32720, housed at the American Museum of Natural History) which preserves the carapace.

[4] This fossil was collected by the American biologist and zoologist William Patten during his extensive explorations at the Rootsikula Formation in Saaremaa, Estonia (then part of the Soviet Union).

[5] It was not until 2008 when during a phylogenetic review of the entire Adelophthalmidae family by the Norwegian Odd Erik Tetlie and German Markus Poschmann paleontologists, N. patteni was recognized as sufficiently different to represent its own genus due to the anterior position of its eyes, much more exaggerated than in the other adelophthalmid genera.

[7] These characteristics have led some authors to question whether Eysyslopterus really represents an adelophthalmid or the sister taxon of a group formed by Pterygotioidea and Adelophthalmoidea, but until more fossil material is found this can not be proven.

[4] Orcanopterus Waeringopterus Grossopterus Eysyslopterus Bassipterus Pittsfordipterus Nanahughmilleria Parahughmilleria Adelophthalmus Hughmilleria Herefordopterus Slimonia Erettopterus Pterygotus Acutiramus Jaekelopterus The single known specimen of Eysyslopterus has been recovered from Silurian deposits of the Ludlow epoch of the Rootsikula Formation of Saaremaa, Estonia.

[4] This formation was the habitat of a fauna of eurypterids, among them Erettopterus laticauda, E. osiliensis, Eurypterus tetragonophthalmus, Mixopterus simonsi and Strobilopterus laticeps.