High-resolution fibre neutron diffraction data were recorded from cellulose samples on a D19 diffractometer at the Institut Laue-Langevin (Grenoble). Highly crystalline cellulose I samples from Cladophora (cellulose I alpha + I beta) or Halocynthia (cellulose I beta) origin were prepared in the form of oriented films. Samples were studied in a hydrogenated form and in a hydrogen-deuterium exchanged deuterated form corresponding to all OH moieties being replaced by ODs. These samples, which diffracted to a resolution of around 0.9 A, gave diffraction diagrams consisting of several hundred independent diffraction spots. Crystalline cellulose II fibres resulting from the mercerization of flax were also studied in a hydrogenated form using NaOH/H2O as mercerizing medium and in a deuterated form using NaOD/D2O. Both of these samples diffracted to around 1.2 A, giving fibre diffraction diagrams slightly less resolved than those of cellulose I, but still consisting of more than one hundred independent diffraction spots. For cellulose I as well as for cellulose II, significant differences between the hydrogenated and deuterated patterns were observed and recorded. These new data should lead to improved structures for cellulose and direct identification of the position of hydrogen atoms involved in hydrogen bonding.