The international transference of personal data protection of a State to other one is a topic of special attention in the Data Protection laws. In this respect, the object of the present study is of analysing, from the optics of the Private International Law, the phenomenon of the international transference of personal data protection in the LOPD, for which dividing from the concept of international transference of personal data protection that establishes the proper LOPD, we will analyse the regime of authorization of the international transferences of personal data protection, the activity of the Spanish Agency of Protection of Information (AEPD) in this matter, and this way to be able to centre on the resolution of the principal questions: a) Judicial International Competition; b) Applicable Law; and, c) Recognition and execution of foreign decisions.