This article is the first of a series of studies about estoppel in arbitration. Since estoppel is a common law doctrine, we consider the continental law system is not familiar with it, but given the globalization of law and the increasing use of arbitration to solve national and international disputes, a study about it must be made, not only for its theoretical interest but also to be used for the lawyers and arbitrators than might face the doctrine in a case or once they know it, they could eventually apply it. This first research, is the product of the project Interpretation and Application of Private Law that has been carried out by the Study Group on private law in Pontificia Universidad Javeriana. The purpose of the article is to show how in some cases it is possible to allow a third party in a subsequent lawsuit to assert collateral estoppel against one of the arbitral parties, through a new interpretation of that doctrine's elements.