The geometrical structures and properties of conjugated polyhelicenes and annelated fused-ring carbon helices with analogous frameworks were theoretically studied at the HF/6-31G and B3LYP/6-31G levels. These studies focused on the stability of the fused-ring structures with special emphasis on the helical geometrical arrangements. To elucidate bonding patterns, the orbitals, electron density contours, and the electrostatic potential of these helical compounds were analyzed. The structure of fused polynaphthalenes arranged in a helical spiral can be regarded as part of a locally helical graphite lattice that is expected to give rise to special electronic properties along the helically layered conjugated single sheet that can be regarded as a single extended pi system but also involving local layer-to-layer pi-pi interactions that are typical in ordinary graphite. This dual feature might lead to novel materials.