The 2nd European AcrossGrids Conference (AxGrids 2004) aimed to examine the state of the art in research and technology developments in Grid Computing, and provide a forum for the presentation and exchange of views on the latest grid-related research results and future work. The conference was organized by Cross Grid, a European Union-funded project on Grid research, GRIDSTART, the EU-sponsored initiative for consolidating technical advances in grids in - rope, and the University of Cyprus. It continued on from the successful 1st European Across Grids Conference, held in Santiago de Compostela, Spain, in February 2003. AxGrids 2004 was run in conjunction with the 2nd IST Conc- tation Meeting on Grid Research, which brought together representatives from all EU-funded projects on Grid research for an exchange of experiences and ideas regarding recent developments in European grid research. The conference was hosted in Nicosia, the capital of Cyprus, and attracted- thors and attendees from all over Europe, the USA, and East Asia. The Program Committee of the conference consisted of 37 people from both academia and - dustry, and there were 13 external reviewers. Overall, AxGrids 2004 attracted 57 paper submissions (42 full papers and 15 short posters). Papers underwent a thorough review by several Program Committee members and external - viewers. After the review, the Program Chair decided to accept 26 papers (out of 42) for regular presentations, 8 papers for short presentations, and 13 - pers for poster presentations. Accepted papers underwent a second review for inclusion this postproceedings volume, published as part of Springer's Lecture Notes in Computer Science series.