This work examines the various issues related to the origin of Linear B script and the adaptation process that led to the creation of this script from the Linear A graphic system. The analysis, based separately on the “external” factors of the writing system (palaeography and pinacological features) and on the “internal” factors (syllabary structure, sematographic heritage, spelling rules) and their reciprocal connections, makes plausible the hypothesis that the process of adaptation that led from Linear A to Linear B took place in a unified manner, both chronologically and geographically. This is in contrast to some recent hypotheses that see the two Linear scripts as the manifestation of a “Cretan writing tradition” that would have passed seamlessly from the recording of the Minoan language to that of Mycenaean Greek.