A sense circuit for serial dichotomic sensing of multiple-level memory cells which can take one programming level among a plurality of m=2.sup.n (n>=2) different programming levels, comprising biasing means for biasing a memory cell to be sensed in a predetermined condition, so that the memory cell generates a cell current with a value belonging to a plurality of m distinct cell current values, each cell current value corresponding to one of said programming levels, a current comparator for comparing the cell current with a reference current generated by a variable reference current generator, and a successive approximation register supplied with an output signal of the current comparator and controlling the variable reference current generator, characterized in that the variable reference current generator comprises an offset current generator permanently coupled to the current comparator, and m-2 distinct current generators, independently activatable by the successive approximation register, each one generating a current equal to a respective one of said plurality of cell current values.