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The Roman Catholic Church holds that a bishop's consecration is valid if the sacrament of Holy Orders is validly done and the consecrating bishop's orders are valid, regardless of whether this takes place within or outside of the Catholic Church. Thus, Catholics recognize the validity of the episcopacy of Eastern Orthodox and Oriental Orthodox bishops. They do not recognize Anglican bishops, because of changes in the rite of Holy Orders in the Anglican churches.
The Eastern Orthodox Church holds that an bishop's consecration is less than fully valid if it is not within the "One Holy Catholic and Apostolic Church", i.e., one of the canonical Eastern Orthodox churches. In many cases, the doctrine of ekonomia is applied to such bishops if they convert to Orthodoxy.