The present paper offers a synopsis of the different scenarios that may give rise to the application of the lis pendens principle in international commercial arbitration, focusing first on parallel proceedings before a domestic court and an arbitral tribunal, and second on parallel proceedings before different arbitral tribunals; it thereby avoids a discussion on parallel actions before arbitral tribunals and supranational bodies, which would step into the turfs of public international law. The first scenario being rather concisely addressed by the New York Convention and national arbitration statutes, this paper devotes a considerable part of the discussion to identifying solutions to the second scenario, and assessing the practicalities (or lack thereof) they might entail.