Greek engineering Schools have a high status and attract good students. However, we show that in the leading institution, the National Technical University of Athens, only 27% of the students admitted in 1992-2003 graduated after the nominal five years study: the median graduation time was 73 months (reaching 93 months in one School) and 12% are predicted never to graduate at all, most without withdrawing officially. Results differ between Schools, between routes of admission and by gender (females being better than males). Systematic study of reasons for not completing or delay in completing studies is urgently needed. Overall, 4% of the students withdraw officially during their first year. The percentage of withdrawals by School is negatively correlated with the percentage that gave that School as first choice in the entrance procedure, indicating problems in the admission system. (Contains 4 figures and 2 tables.)