We consider the distributed construction of a minimum weight 2-edge-connected spanning subgraph (2-ECSS) of a given weighted or unweighted graph. A 2-ECSS of a graph is a subgraph that, for each pair of vertices, contains at least two edge-disjoint paths connecting these vertices. The problem of finding a minimum weight 2-ECSS is NP-hard and a natural extension of the distributed MST construction problem, one of the most fundamental problems in the area of distributed computation. We present a distributed \frac32 \frac{3}{2} -approximation algorithm for the unweighted 2-ECSS construction problem that requires O( n ) communication rounds and O( m ) messages. Moreover, we present a distributed 3 -approximation algorithm for the weighted 2-ECSS construction problem that requires O( n logn ) communication rounds and O( n log² n + m ) messages.