Connexionalism (the modernised spelling Connectionalism is rare in British Methodism) is the theological understanding and foundation of Methodist polity, as practised in the British Methodist Church, the American United Methodist Church, and in many of the countries where Methodism was established by missionaries sent out from these two Churches. In the American church, where bishops are used, connexionalism is a variety of episcopal polity; however, in some countries the title of bishop may be used without any change in the Connexional polity. In world Methodism, a given Connexion is usually autonomous.
In the history of Christianity in England, a connexion was a circuit of prayer groups who would employ travelling ministers alongside the regular ministers attached to each congregation. This method of organising emerged in eighteenth century English Non-conformist religious circles; this is why the otherwise old-fashioned spelling (connexion rather than connection) is retained. The Countess of Huntingdon's Connexion, for instance, was founded by Selina, Countess of Huntingdon. Over time, as Methodism became a separate church, this structure of connexions came to form a new system of polity, separate from episcopal polity.
Connexional polity in Britain has always been characterized by a strong central organisation which holds an annual Conference. The connexion is divided into Districts in the charge of a Chairman. In other countries the Chairman is sometimes called a Bishop, or District Bishop. Methodist districts often correspond approximately, in geographical terms, to counties – as do Church of England dioceses. The districts are divided into circuits governed by the Circuit Meeting and led and administrated principally by a superintendent minister. Ministers are appointed to Circuits rather than to individual churches. Most notably, there are no bishops in the British connexion. 
American Methodist churches are generally organized on a connexional model, related but not identical to that used in Britain. Pastors are assigned to congregations by bishops, distinguishing it from presbyterian government. Methodist denominations typically give lay members representation at regional and national meetings (conferences) at which the business of the church is conducted, making it different from most episcopal government. This connexional organizational model differs further from the congregational model, for example of Baptist, and Congregationalist churches, among others.
The United Methodist Church website defines "connexion" as the principle that:
See also 
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