Since Einstein’s first publication on relativity many papers have been published on the logical derivation of the Lorentz transformations, but apparently without any conclusiveness on the subject having been reached. In this paper, by basing the analysis of this problem on purely kinematic postulates that can be shown to be necessary, an attempt is made to achieve a degree of definitiveness in the results that would enhance their usefulness in ongoing studies on the conceptual foundations of relativistic physics.