This encephalopathy is characterized by an important artheriosclerotic involvement of the vessels of the cerebral white matter and a difuse subcortical demyelination, sparing the cortex. The diagnosis is presently possible, ante mortem, by connecting the clinical picture with the CT scan findings, which are essential. Three cases with Binswanger encephalopathy are reported and the following picture was found: age 50 to 70 years old at the onset; dementia with scanty neurological signs; systhemic arterial hypertension; subacute course of the disease; and a CT scan, highly characteristic, that shows bilateral and symmetric subcortical hypodensity. In one of the patients, that eventually died, an angiography disclosed a right internal carotid thrombosis and a diminished flow in the thalamic striate arteries in both sides. The other two patients are aparently stabilized with anti-hypertensive medication. Binswanger encephalopathy is still seldom described in spite of being a very well defined entity. This diagnosis should be considered much more frequently because it is possible to prevent the encephalopathy avoiding systemic hypertension that is probably intimately linked with the genesis of the disease.