This study reports for the first time crystal-structure data for amosite and fibrous anthophyllite. The chemical composition of the two fibre species was determined from EMPA. Crystal structures were refined using powder-diffraction data, using both laboratory sources and synchrotron radiation. Results were compared with the available literature data for the non-fibrous varieties grunerite and anthophyllite, respectively. The calculated site-occupancies for all samples are in agreement with the chemical compositions calculated from EMPA. The existing structure models of grunerite and orthorhombic anthophyllite also applies to the corresponding fibrous varieties amosite and fibrous anthophyllite, respectively. In amosite, both Fe2+ and Fe3+ atoms are found at the sites M(1), M(2) and M(3) and Fe2+ ions is the only atomic species found at site M(4). Mg is disordered over the C sites with a preference for site M(2). Minor Ca and Na have been assigned to the A site. In fibrous anthophyllite, Mg is the only atomic species found at the M1, M2 and M3 sites. Fe2+, Mg (and minor Mn) have been assigned to the M4 site, whereas minor Ca has been assigned to the A site. In both structures, the environment at the M(4) site in amosite and M4 site is in fibrous anthophyllite highly distorted. This work can be considered a basis for studies aimed at understanding the potential toxicity/pathogenicity of these mineral fibres.