The extended Hiickel method within the tight-binding approximation was applied to two benzoxazole polymers of a type much studied because of their excellent mechanical properties. Specifically, band structure calculations were carried out in part to identify the most stable conformation of the polymers in the crystalline state. In the preferred conformation of one polymer the rotational angle between the bibenzoxazole groups is 20", and that between the bibenzoxazole group and thep-phenylene group is 0". The other polymer consists simply of benzoxazole groups, and these are predicted to be coplanar, The above conformational predictions are in excellent agreement with the results of both experimental and theoretical studies on relevant model compounds. In addition, the band gaps in the axial direction were found to be 1,86 and 2,31 eV, respectively, and these values are close to the corresponding experimental values 1,4 to 1,s eV reported for trans-polyacetylene. In both benzoxazole polymers the band gap was found to increase with increase in nonplanarity due to the concomitant reduction in charge delocalization.