Before revision:  First, we extend the results of [ 32 ] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of upper obstacles. Then, under some regularity assumptions on one of the barriers, similar to the ones in [ 9 ], and when the two barriers are completely separated, we provide a complete wellposedness theory for doubly reflected second-order BSDEs.
After revision:  First, we extend the results of [ 32 ] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar to the ones in [ 9 ], and when the two barriers are completely separated, we provide a complete wellposedness theory for doubly reflected second-order BSDEs.