The histological composition of the galeaspid cephalothoracic skeleton has been much debated: here we attempt to resolve this through the analysis of well-preserved remains of galeaspids from Yunnan Province, and Tarim Basin, Xinjiang Uygur Autonomous Region, China. Our results indicate that the galeaspid dermoskeleton is dominantly composed from an acellular laminar bone in which the mineral is organised into cylindrical crystal bundles that are arranged into three orthogonal sets with associated extrinsic fiber spaces, a unique histology for which the term galeaspedin is coined. This is permeated by a coarse vascular plexus that divides the dermoskeleton into upper and lower zones, and the upper zone into distinct tesserae which, like the bounding vascular network, are polygonal in outline.The outer surface of the dermoskeleton is ornamented by a series of tubercles centered on tesserae, the latter composed partly from galeaspedin, and partly from a capping layer of microspherulitic, acellular bone, similar to the limiting layer of bone of elasmoid scales. Neither dentine nor enameloid is present, nor do the tissue compositions or their arrangement indicate an odontogenic origin.The endoskeleton is composed of an outer zone of globular calcified cartilage in contact with the dermoskeleton through a poorly mineralized intermediate zone. The inner zone is finely laminated, resulting from progressive zones of calcification embracing the calcospherites in a direction away from the dermoskeleton. There is no persuasive histological evidence for the presence of appositional perichondral bone. As in osteostracans, the galeaspid endoskeleton is interpreted as an expanded neurocranium. However, the presence of a calcified cartilaginous neurocranium in galeaspids in the absence of a perichondral bone layer indicates that these two histogenic components have distinct evolutionary origins. The presence of perichondral bone is a synapomorphy of osteostracans and jawed vertebrates, while the presence of a mineralized neurocranium unites galeaspids to this clade (possibly also including pituriaspids).