Tissues from adult Sprague-Dawley rats fixed by perfusion with buffered aldehydes for a combined study of the vascular system of the brain are described in light and electron microscopy. In these preparations lack of shrinkage prevents the formation of perineuronal and perivascular spaces. However, connective tissue stains indicate restricted tissue space along the course of small arteries and veins. In fine structure this space is found within the walls of the vessels. It consists of a tubular extension of tissue space bounded inwardly by the endothelial boundary (basement) membrane and outwardly by the neural boundary membrane. Between these boundaries the formed elements of the media and the adventitia are found. The media consists of a thin layer of smooth muscle cells; each cells being enclosed in its own boundary membrane. The adventitia consists of cells and fibrous elements of the connective tissues which are derived, near the surface of the brain, from the intermingling of pial and vascular leptomeninges. This “neural” portion of the tissue space extends from the depths of the capillary bed (where it is obliterated by the fusion of boundary membranes), along the course of the blood vessels, through the subarachnoid space and into the general tissue space of the body.