Composability and deadlock-freedom are important properties that are stated for transactional memory (TM). Commonly, the Semantics of TM requires linearization of transactions. It turns out that linearization of transactions that have cyclic communication brings incomposability and deadlock. Inspired from TM and Actors, this work proposes Transactors that provide facilities of isolation from TM and communication from Actors. We define the semantics of Transactors including support for cyclic transactional communication. An algorithm implementing this semantics is offered. The soundness of the algorithm is proved.