The deals with John Angelicoussis companies was signed in Athens during a visit by Sung-leep Jung president of DSME to attend Posidonia.
The 318,850 dwt VLCCs are priced at $84.6m a piece while the 180,000 cu m LNG are $185m in each.
This potentially makes the deal an over $1bn shot in the arm for DSME.
The orders come during a week when many Greek owners such as Nikolas Tsakos have made a plea for shipowners to invest in secondhand tonnage rather than newbuildings for the sake of the health of the market.
Prior to the latest orders by Maran just 300 newbuildings had been ordered worldwide this year.