Tabled evaluations can incorporate a number of features, including tabled negation, reduction with respect to the well-founded model, tabled constraints and answer subsumption. Many of these features are most efficiently evaluated using the Local evaluation strategy, which fully evaluates each mutually dependent set of tabled subgoals before returning answers to other subgoals outside of that set. In this paper, we introduce a formalism, Concurrent Local SLG by which multiple threads of computation concurrently perform Local evaluation of the well-founded semantics, and which is a framework for multi-threaded tabling in the XSB system. We prove several properties of Local evaluation within single-threaded tabled computation. We then extend SLG to a model of concurrency and show that the completeness and complexity of SLG are retained when computed by multiple threads. Finally, we extend Local evaluation to concurrent SLG, and show that the properties of Local evaluation continue to hold under concurrency.