Angular dependence of X-ray emission and absorption spectra was measured for both graphite and films of carbon nanotubes (CNTs) oriented perpendicular to the substrate surface. The ratio of intensities of and peaks in the X-ray spectra of CNT films was found to depend not only on the orientation of nanotubes but also on the orientation of graphite-like layers inside multi-walled nanotubes. Fluorescence measurement for the samples also showed the dependence on the degree of CNT alignment as well as on the texture of CNT layers. A possibility of X-ray photon propagation in CNTs in the conditions of anomalous dispersion near the C K-edge is discussed.