A machine for the orderly storage and delivery of banknotes comprises an input of banknotes (11), an output of banknotes (19), a path (12, 14, 15, 18) of sequential flow of banknotes between the input and the output, devices (13) for detecting the characteristics of the banknotes along said path and a plurality of compartments (20) for the internal storage of the banknotes. Each compartment (20) of the plurality is a sequential drum compartment and winding belts and the compartments of the plurality are divided into two series of compartments (16, 17). The internal path of the banknotes between input and output comprises a sorting section (15) along which the inputs/outputs of the two series of compartments of the plurality face each other alternately on two opposite sides, each input/output being associated to sorting means (25) that can be commanded for the deviation of the banknotes between the sorting path (15) and the compartment (20) associated.