Thirty-four fossil insect wings from the Fur Formation of Denmark (Eocene-Paleocene transition) are recognised as neuropteran forewings standing close to extant Psychopsidae (silky lacewings). This affinity is based primarily on their possession of a vena triplica in the forewing. A new genus, Palaeopsychops gen. n. and four new species, P. latifasciatus sp. n. (type species), P. abruptus sp. n., P. angustifasciatus sp. n. and P. maculatus sp. n. are described. Palaeopsychops is identified mainly by the shape of vena triplica and costal space and by the venation of radial space. The new genus appears most closely related to some fossil species of the North American Eocene, while it appears only remotely related to the psychopsid genus Propsychopsis Krüger described from Baltic amber (European Eocene). The different species of Palaeopsychops are separated on relatively minor differences in wing venation and pigmentation. The entire fossil record of psychopsid-like Neuroptera are reviewed and issues of phylogeny and zoogeography are discussed. A total of 5 extant and 21 fossil genera are recognised in the Psychopsidae lineage based on an extended vena triplica definition. The lineage goes back at least to the Upper Triassic. An attempt is made to gather the psychopsid genera into larger natural entities. Extant Psychopsidae are restricted to S. Africa, Australia and SE. Asia. It is suggested that the present relictual distribution is mainly caused by extinction events.