National authorities in the Member States experience difficulties in identifying illegally staying third-country nationals or stateless persons with a view to their return and readmission. It is therefore essential to ensure that data on third-country nationals or stateless persons who are staying illegally in the Union are collected and transmitted to Eurodac and are also compared with data collected and transmitted for the purpose of establishing the identity of applicants for international protection and of third-country nationals or stateless persons apprehended in connection with the irregular crossing of the external borders of the Member States, in order to facilitate their identification and re-documentation, to ensure their return and readmission, and to reduce identity fraud. That collection, transmission and comparison of data should also contribute to reducing the length of the administrative procedures necessary for ensuring the return and readmission of illegally staying third-country nationals or stateless persons, including the period during which they may be kept in administrative detention awaiting removal. It should also enable the identification of third countries of transit, where the illegally staying third-country national or stateless person may be readmitted.