Most living vertebrates are jawed vertebrates (gnathostomes), and the living jawless vertebrates (cyclostomes), hagfishes and lampreys, provide scarce information about the profound reorganization of the vertebrate skull during the evolutionary origin of jaws(1-9). The extinct bony jawless vertebrates, or 'ostracoderms', are regarded as precursors of jawed vertebrates and provide insight into this formative episode in vertebrate evolution(8-14). Here, using synchrotron radiation X-ray tomography(15,16), we describe the cranial anatomy of galeaspids, a 435-370-million-year-old 'ostracoderm' group from China and Vietnam(17). The paired nasal sacs of galeaspids are located anterolaterally in the braincase, and the hypophyseal duct opens anteriorly towards the oral cavity. These three structures (the paired nasal sacs and the hypophyseal duct) were thus already independent of each other, like in gnathostomes and unlike in cyclostomes and osteostracans (another 'ostracoderm' group), and therefore have the condition that current developmental models regard as prerequisites for the development of jaws(1-3). This indicates that the reorganization of vertebrate cranial anatomy was not driven deterministically by the evolutionary origin of jaws but occurred stepwise, ultimately allowing the rostral growth of ectomesenchyme that now characterizes gnathostome head development(1-3).