In this paper we present TAL-C, a logic of action and change for worlds with action concurrency. TAL-C has a first-order semantics and proof theory. It builds on an existing logic TAL, which includes the use of dependency laws for dealing with ramification. It is demonstrated how TAL-C can represent a number of phenomena related to action concurrency: action duration, how the effects of one action interferes with or enables another action, synergistic effects of concurrent actions, conflicting and cumulative effect interactions, and resource conflicts. A central idea is that actions are not described as having effects that directly alter the world state. Instead, actions produce influences, and the way these influences alter the world state are described in specialized influence laws. Finally, we address how TAL-C narratives can be written to support modularity.