Five cases are reported of patients with so-called primary progressive apraxia, defined as a slowly worsening disturbance of gestural abilities, without other major cognitive changes during a long period, in relation to degenerative cortical atrophy. All five cases, as other cases in the literature, share the following common features: 1) asymmetrical onset of upper limb clumsiness, more often involving the left side, later involving the contralateral side and lower limbs; 2) after a variable delay, the occurrence of symptoms suggesting subcortical involvement (akinesia, limb stiffness, various kinds of movement disorders, dystonia, paresis of vertical gaze); 3) diffuse cortical atrophy typically more pronounced in the superior parietal cortex opposite to the first side affected. The unusual nature of apraxia in all these cases is pointed out and referred to as Luria's "kinesthaesic apraxia", ascribed to a loss of "selectivity" of distal elementary movements. This pattern of symptoms and their specific outcome could represent a distinct entity.