The situation in the world art-market in the period from 2002 up to the present date is considered in the work: data ofvalue and volume of transactions of the global art-market are given; the phenomenal rise of the Chinese market, the stability of the US market and the european art-market falling are stressed. The history and the development ofthe world’s leading art fair — The European Fine Art Fair (TEFAF, Maastricht) — are given. The results of TEFAF 2014 are considered. The following trends of the global art-market have been discovered: the permanent demand of all participants for old masters; significant market growth due to the sails of the very expensive art-objects while a total number of transactions is decreasing; raising interest to the art-objects from China and Japan; the increasing demand for expensive works of arts and crafts and antiques.