This thesis examines the different methodologies at work within the Irish Anglican-Methodist dialogue from 1965 to 2002 by using the Wesleyan Quadrilateral as a heuristic tool. Through the lens of Scripture, tradition, reason, and experience, it illustrates the similarities and differences between Irish Anglicans and Irish Methodists on the nature and role of the sources by critically examining the key texts of the ecumenical dialogue. It reveals new insights into how the ecumenical process developed and how participants both used and understood the sources in particular ways in their methodologies. Through the lens of the Wesleyan Quadrilateral the research examines the primary source material of the three phases of the dialogue: 1. The Bipartite Conversations 1965-1968, 2. The Tripartite Consultation 1968-1988, and, 3. The Joint Theological Working Party 1989-2002. It finds that when individual Irish Anglicans and Irish Methodists write theology to present the doctrinal position of their respective church, they use the sources in denominational. ways. Their understanding and employment of the sources reflects that of the wider denominational tradition in which they reside. It shows that convergence took place during each phase of the dialogue as Irish Anglicans and Irish Methodists worked together to develop shared and agreed positions. It also charts the location of Irish Anglicans and Irish Methodists on the spectrum of theological opinion at various points in the dialogue. It highlights the potential that existed for the development of a common theological method incorporating the four sources, and the failure to formally realise this. And it suggests that the Wesleyan Quadrilateral could provide Irish Anglicans and Irish Methodists with what they need for the ecumenical future