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Dual-energy CT (DECT) with scans over limited-angular ranges (LARs) may allow reductions in scan time and radiation dose and avoidance of possible collision between the moving parts of a scanner and the imaged object. The beam-hardening (BH) and LAR effects are two sources of image artifacts in DECT with LAR data. In this work, we investigate a two-step method to correct for both BH and LAR artifacts in order to yield accurate image reconstruction in DECT with LAR data. From low- and high-kVp LAR data in DECT, we first use a data-domain decomposition (DDD) algorithm to obtain LAR basis data with the non-linear BH effect corrected for. We then develop and tailor a directional-total-variation (DTV) algorithm to reconstruct from the LAR basis data obtained basis images with the LAR effect compensated for. Finally, using the basis images reconstructed, we create virtual monochromatic images (VMIs), and estimate physical quantities such as iodine concentrations and effective atomic numbers within the object imaged. We conduct numerical studies using two digital phantoms of different complexity levels and types of structures. LAR data of low- and high-kVp are generated from the phantoms over both single-arc (SA) and two-orthogonal-arc (TOA) LARs ranging from 14∘ to 180∘. Visual inspection and quantitative assessment of VMIs obtained reveal that the two-step method proposed can yield VMIs in which both BH and LAR artifacts are reduced, and estimation accuracy of physical quantities is improved. In addition, concerning SA and TOA scans with the same total LAR, the latter is shown to yield more accurate images and …