A method of electrical testing electronic devices DUT, comprising: connecting at least an electronic device DUT to an automatic testing apparatus suitable for performing the testing of digital circuits or memories or of digital circuits and memories; sending electrical testing command signals to the electronic device DUT by means of the ATE apparatus; performing electrical testing of the electronic device DUT by means of at least one advanced supervised self testing system “Advanced Low Pin Count BIST” ALB which is built in the electronic device DUT, the ALB system being digitally interfaced with the ATE through a dedicated digital communication channel; and sending reply messages, if any, which comprise measures, failure information and reply data to the command signals from the electronic device DUT toward the ATE apparatus by means of the digital communication channel.