As I mentioned the other day, the Episcopal Church does have nuns and monks included as part of our spiritual organization.  More precisely, the Church has included religious orders [and celibate clergy] for its entire history.  Your Rector, who is a former member of the Society of St. Barnabas, a religious order that was dissolved some twenty years ago, credits his ecclesiology to his early monastic training.  Not to mention his difficulty in taking days off or scheduling vacations.
[Our monastery, St. Barnabas House, is pictured above. It now serves as an assisted living facility.] 
A complete official list may be found here.
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