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 peri-chronosopheme. 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'.