Deep-freezing apparatus for foodstuffs comprising: - a deep-freezing compartment, - sensor means configured to detect a temperature inside the foodstuffs stored in said deep-freezing compartment, - processing means for signals generated by said sensor means, - display means for displaying information worked out and output by said processing means, characterized in that it further comprises: - a neural network configured to receive the signals issued by said processing means for the signals from said temperature sensor means, - and by a plurality of information pieces on a duration of successive time intervals, each one of which measures the time elapsing for going from a respective first temperature down to a respective second temperature, and configured to provide information relating to a residual time (t r) that is still needed for the temperature inside the foodstuff being deep-frozen to reach down to a pre-set, still lower temperature value (T c), at which there corresponds a state transition phase of the same foodstuff, and in that said processing means are configured to receive said residual time (t r) from said neural network and provide in response thereto an information representative to a predicted time (t n) needed for a pre-determined temperature lying below said state transition temperature (T c), and measurable by said sensor means, to be eventually reached, wherein said pre-determined temperature is a deep-freezing temperature lying significantly below 0°C, wherein said processing means are configured such that, at a general instant (T x), they: - determine the time (t 1) elapsed for the temperature detected by said sensor means to decrease from a first temperature value (T a1) to a second temperature value (T a2) lying below said first temperature value (T a1), and - the time (t 2) elapsed for the temperature detected by said sensor means to decrease from a third temperature value (T a3) to a fourth temperature value (T a4) lying below said third temperature value (T a3), - input said times (t 1) and (t 2), as well as an actual temperature value (T pres) measured by the sensor at the moment of said processing step, in said neural network, which is in turn configured to determine the residual time (t r) still needed for the temperature to reach down to the pre-set value (T c), - calculate an initial time (t f) as the sum of the time (t a) elapsed up to the measurement instant and the corresponding residual time (t r), - process said initial time (t f) by comparing it with previously stored information configured to provide the duration of a total time (t t) of the deep-freezing process based on said initial time (t f). - a deep-freezing compartment, - sensor means configured to detect a temperature inside the foodstuffs stored in said deep-freezing compartment, - processing means for signals generated by said sensor means, - display means for displaying information worked out and output by said processing means, - a neural network configured to receive the signals issued by said processing means for the signals from said temperature sensor means, - and by a plurality of information pieces on a duration of successive time intervals, each one of which measures the time elapsing for going from a respective first temperature down to a respective second temperature, and configured to provide information relating to a residual time (t r) that is still needed for the temperature inside the foodstuff being deep-frozen to reach down to a pre-set, still lower temperature value (T c), at which there corresponds a state transition phase of the same foodstuff, and in that said processing means are configured to receive said residual time (t r) from said neural network and provide in response thereto an information representative to a predicted time (t n) needed for a pre-determined temperature lying below said state transition temperature (T c), and measurable by said sensor means, to be eventually reached, - determine the time (t 1) elapsed for the temperature detected by said sensor means to decrease from a first temperature value (T a1) to a second temperature value (T a2) lying below said first temperature value (T a1), and - the time (t 2) elapsed for the temperature detected by said sensor means to decrease from a third temperature value (T a3) to a fourth temperature value (T a4) lying below said third temperature value (T a3), - input said times (t 1) and (t 2), as well as an actual temperature value (T pres) measured by the sensor at the moment of said processing step, in said neural network, which is in turn configured to determine the residual time (t r) still needed for the temperature to reach down to the pre-set value (T c), - calculate an initial time (t f) as the sum of the time (t a) elapsed up to the measurement instant and the corresponding residual time (t r), - process said initial time (t f) by comparing it with previously stored information configured to provide the duration of a total time (t t) of the deep-freezing process based on said initial time (t f).