We present an algorithm for the computation of 2'-deoxyribose-phosphodiester backbone conformations that are stereochemically compatible with a given arrangement of nucleic acid bases in a DNA structure. The algorithm involves the sequential computation of 2'-deoxyribose and phosphodiester conformers (collectively referred to as a backbone 'segment'), beginning at the 5'-end of a DNA strand. Computation of the possible segment conformations is achieved by the initial creation of a fragment library, with each fragment representing a set of bond lengths, bond angles and torsion angles. Following exhaustive searching of sugar conformations, each segment conformation is reduced to a single vector, defined by a specific distance, angle and torsion angle, that allows calculation of the O(1)' position. A given 'allowed' conformation of a backbone segment is determined based on its compatibility with the base positions and with the position of the preceding backbone segment. Initial computation of allowable segment conformations of a strand is followed by the determination of continuous backbone solutions for the strand, beginning at the 3'-end. The algorithm is also able to detect repeating segment conformations that arise in structures containing geometrically repeating dinucleotide steps. To illustrate the utility and properties of the algorithm, we have applied it to a series of experimental DNA structures. Regardless of the conformational complexity of these structures, we are able to compute backbone conformations for each structure. Hence, the algorithm, which is currently implemented within a new computer program NASDAC (Nucleic Acids: Structure, Dynamics and Conformation), should have generally applicability to the computation of DNA structures.