1. The Place of Decisional Harmony and Procedural Efficiency within the Brussels I Regime: The Rules on Parallel Proceedings and their Evolution over Time.- 2. Lis Pendens and Related Actions Involving a Court in a Third Country: Articles 33 and 34 of the Brussels I-bis Regulation in a Nutshell.- 3. The Reasons for Elaborating a Uniform Set of Rules of European Union Law Dealing with Extra-European Lis Pendens and Related Actions.- 4. Some Remarks on the Operation of the New Provisions: (a) The Conditions on which Proceedings May Be Stayed.- 5. (b) The Conditions on which the Claim Should, or Could, Be Dimissed Once a Decision on the Merits Has Been Rendered in the Third Country.- 6. (c) The Coordination of the Rules on Extra-European and Intra-European Lis Pendens and Related Actions.- 7. Concluding Remarks.