Rail union the RMT has suspended planned strikes tomorrow and on November 7 and 9.
They will now enter into a period of intensive negotiations with Network Rail and the train operating companies.
The strikes would have stopped all services through Totnes and Ivybridge on strike days themselves and caused disruption on days around those days.
RMT has secured unconditional talks on Network Rail and the promise of an offer from the train operating companies .
The current dispute continues, and the union is continuing to re-ballot members to secure a fresh mandate for industrial action with the result due on November 15.
RMT general secretary Mick Lynch said: “The threat of strike action and our strongly supported industrial campaign has made the rail employers see sense.
“We have always wanted to secure a negotiated settlement and that is what we will continue to push for in this next phase of intensive talks.
“Our priority is our members, and we are working towards securing a deal on job security, a decent pay rise and good working conditions.
“Our re-ballot remains live and if we have to take strike action during the next six months to secure a deal, we will.”