The paper offers the first and the most comprehensive outline of perichronosophy, i.e. a theory of timelessness and its practicing, which are to be taken as a theoretical (perichronology) and practical (atemporalistics) grounds of syncriticism. The fundamental concept of perichronosophy is perichrony expressed by the term perichronosopheme. This concept has been articulated in recent years by applying the syncritic method in the examination of various pre-temporal, intra-temporal, and beyond-temporal units of timelessness, as well as their various timeless qualities, linkages and processes taking place in various spheres of timelessness: in pre-temporality, intra-temporality as well as between time and timelessness. Perichronosophy goes back mainly to Plato’s theory of timelessness oscillating around the notions of exaiphnes and metaxy.