Bideford will host Torquay on Tuesday in the first match of the inaugural Errea South West Challenge Cup.
There are eight teams in the event, with each side guaranteed two games before the semi-finals are played on Saturday, with the final on Sunday.
Championship side Crystal Palace, who are currently managed by former Plymouth Argyle boss Neil Warnock, will be favourites to win.
Yeovil Town, from League One, will be another of the fancied teams.
They start against Blue Square Premier side Kidderminster Harriers on Wednesday.
Other clubs in the tournament include Barnstaple Town, Blue Square South team Eastleigh and Chertsey Town.
All games will be held at Bideford's Sports Ground and Appledore's Churchill Way.
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