A sense circuit for reading EPROM and ROM type memory cells employs a circuit for generating an offsetting current which is exempt of error during transients and which thus permits to achieve a reduced access time. On the other hand, the sense circuit maintains the intrinsic advantages of a current-offset sensing architecture which is represented by a substantially unlimited operating voltage range toward the maximum value VCC.sub.max. The current generating circuit is driven by means of a supplementary row of cells which is decoded at every reading and which replicates, during transients, the behaviour of the row selected for the reading.