We present an extension of the planning framework based on action graphs and local search to deal with PDDL2.1 temporal problems requiring concurrency, while previously the approach could only solve problems admitting a sequential solution. The paper introduces a revised plan representation supporting concurrency and some new search techniques using it, which are implemented in a new version of the LPG planner. An experimental analysis indicates that the proposed approach is suitable to temporal planning with requiring concurrency and is competitive with state-of-the-art planners.