This is a guide catheter assembly. The guide catheter assembly is used to cooperate with a micro-catheter in accessing a tissue target within the body, typically a target which is accessible through the vascular system. Central to the invention is the use of a braided metallic reinforcing member, situated within the catheter body in such a way to create a catheter section having an exceptionally thin wall, controlled stiffness, and high resistance to kinking. The catheter has a terminal segment which is not supported by a braid and the polymer making up that terminal segment is either the same hardness as is the polymer making up the outer covering of next more adjacent section or, preferably, the polymer is harder than is the polymer making up the segment located just proximally of that terminal segment. The braid may have a single pitch or may vary in pitch along the axis of the catheter or catheter section. The braided reinforcing member typically is embedded in a flexible outer tubing member. An inner tubing member is lubricious.