The crystal and molecular structure, together with the hydrogen-bonding system in cellulose I(alpha), has been determined using atomic-resolution synchrotron and neutron diffraction data recorded from oriented fibrous samples prepared by aligning cellulose microcrystals from the cell wall of the freshwater alga Glaucocystis nostochinearum. The X-ray data were used to determine the C and O atom positions. The resulting structure is a one-chain triclinic unit cell with all glucosyl linkages and hydroxymethyl groups (tg) identical. However, adjacent sugar rings alternate in conformation giving the chain a cellobiosyl repeat. The chains organize in sheets packed in a "parallel-up" fashion. The positions of hydrogen atoms involved in hydrogen-bonding were determined from a Fourier-difference analysis using neutron diffraction data collected from hydrogenated and deuterated samples. The differences between the structure and hydrogen-bonding reported here for cellulose I(alpha) and previously for cellulose I(beta) provide potential explanations for the solid-state conversion of I(alpha) --> I(beta) and for the occurrence of two crystal phases in naturally occurring cellulose.