This essay on applicable law in CAS arbitration proceedings, written in Spanish, deals with the private international law issues related to the choice and conflict of laws in arbitration proceedings before the international Court of Arbitration for Sport. First of all, the article examines the issues related to the "lex arbitri", i.e. the law applicable to the procedural aspects of CAS arbitration proceedings, underlining the relevance of Swiss law due to the fact that all CAS proceedings have their legal seat in Switzerland. Then, the issues related to the "lex causae", i.e. the rules of law applicable to substantive matters, are analysed in depth. The "iura novit curia" principle and the various choice-of-law criteria listed by the CAS Code in reference to the four types of CAS arbitration proceedings (ordinary, appellate, Olympic and anti-doping) are thoroughly analysed, underlining the great relevance that private rules of law, not pertaining to any State legislation, have in the sports sector. In this context, the article also carefully examines the etymology, definition and concrete meaning of the controversial "lex sportiva" notion. Finally, the article deals with the limits to the application of the pertinent rules of law deriving from State mandatory norms and public policy principles.