A series of copoly(ester imide)s (CPEIs) was synthesized by the esterification of N,N’-dodecane-1,12-diylbis(trimellitimide) to two different acetylated diols, 4,4’-dihydroxybiphenyl and hydroquinone, in varying proportions. On the basis of their compositions, six samples are designated as CPEI(A-F), in which CPEI(A) is a homopolymer having 100% of incorporated 4,4’-dihydroxybiphenyl and CPEI(F), a homopolymer having 100% of incorporated hydroquinone. The composition ratios of the copolymers are 80/20 (B), 60/40 (C), 40/60 (D), and 20/80 (E). Except for CPEI(F), the five CPEI(A-E)s show enantiotropic liquid crystalline behavior during cooling from the isotropic melt. In all of the samples, highly ordered smectic crystal phases are assumed in the solid state. In the course of structural identification, it has been found that CPEI(A-E)s often exhibit anomalous wide-angle X-ray diffraction (WAXD) fiber patterns : the smectic layer normal is perpendicular to the fiber direction while the (hkO) reflections exhibit maxima along the meridian. Furthermore, the degree of orientation for the (hkO) reflections is apparently much lower than that of the layer structure. Crystallographic analysis is given to provide a quantitative explanation of experimentally obtained WAXD fiber patterns.