A system for curing polymer matrix composite parts out of autoclave in manufacturing and repairing processes including: (i) an inner vacuum bag (3) placed over the lay-up to be cured located over a working area (15, 18) with the edges of the inner vacuum bag (3) joined to the working area by first sealing elements (8); (ii) a Perforated bulkhead (4) located over the inner vacuum bag (3), (iii) an Outer vacuum bag (2) over a perforated bulkhead (4) and over the edges of the inner vacuum bag with the edges of the outer vacuum bag (2) joined to the working area (15, 18) by second sealing elements (1), (iv) a vacuum device (5, 7, 6) and (v) a heating source (9, 20).