In this paper, two‐hop parallel N‐relay networks are considered and the diversity‐multiplexing tradeoff (DMT) is derived over Gamma‐Gamma free‐space optical (FSO) channels with identical average received signal to noise rations in all links. In the derivations, both local and global channel state information (CSI) are investigated. In the local CSI case, the node only knows its incoming link conditions, while in the global CSI case, the nodes are aware of all the CSIs in the network. The listening and transmitting times at the relays as variables in the DMT derivation are further considered which are later used to optimize the performance of the network. It is demonstrated that the optimal DMT is obtained with the static quantize map and forward (SQMF) and dynamic quantize map and forward (DQMF) strategies for different ranges of the multiplexing gain. In addition, the optimal schedule of relays in the DQMF strategy is determined as a function of the local channel conditions in the relays.