Cis-Golgi cisternae have a higher freeze-fracture particle density than trans-cisternae. Transport vesicles neighboring cis or trans positions of the Golgi stack have a particle concentration comparable to that of the adjacent cisterna and the buds emerging from it. This implies that transport vesicles remain locally within the stack during their lifetime, near their origin, favoring a processive pattern of transport in which vesicle transfers occur preferentially between adjacent cisternae in the stack. A "string theory" is proposed to account for processive transport, in which a carpet of fibrous attachment proteins located at the surface of cisternae (the strings) prevent budded vesicles from diffusing away but still allow them to diffuse laterally, effectively limiting transfers to adjoining cisternae in the stack. Fibrous elements that multivalently connect otherwise free COPI-coated vesicles and uncoated transport vesicles to one or two cisternae simultaneously are discerned readily by electron microscopy. It is suggested that long, coiled coil, motif-rich, Golgi-specific proteins including p115, GM130, and possibly giantin, among others, function as the proposed strings.