The snout and mouth-parts of Rhinopteraspis cornubica (McCoy) (syn. R. dunensis (Roemer)) are described for the first time in specimens from Daleszyce (Central Poland) and Overath (Rhineland). An analysis is made of the various types of snout known in the pteraspids, and diagnoses are given of important genera based on this feature. Evolutionary trends within the pteraspids are outlined, and it is demonstrated th at the long-snouted condition was achieved in two distinct ways. It is suggested that the possession of double nasal sacs excludes the pteraspidomorphs (heterostraci) from the ancestry of the myxinoid cyclostomes.