On the occasion of the transfer of the Physics Department of the Florence University to the new scientific campus in Sesto Fiorentino, INFN decided in 2001 to provide our group with a, large laboratory dedicated to applications of nuclear techniques, based on a new 3 MV Tandetron accelerator, which would greatly improve the performance of existing Ion Beam Analysis (IBA) applications (for which we were using since the 1980s an old single-ended Van de Graaff) and in addition would start an activity of Accelerator Mass Spectrometry (AMS), in particular for C-14 dating. The new laboratory, LABEC, is hosted in a dedicated building purposely constructed by the University of Florence. LABEC has been installed within three years from the decision to fund it, and after a commissioning phase has become in 2004 fully operational for both IBA and AMS. Switching between the two kinds of operation is very easy and fast, which allows us high flexibility in programming the activities. The paper shortly describes the facilities presently available in the laboratory, their technical features and some recent applications.