A theory describing relaxation properties (manifested in dielectric relaxation) of rigid rods possessing a dipole moment and embedded in a polymer network was constructed. The dynamics of short rods and of rods comparable to the contour length of a polymer chain between rod junctions was considered. The frequency dependences of permittivity were obtained. The shape of the relaxation spectrum and the relaxation times were studied in relation to the ratio between the lengths of the rod and interjunction chain segments, the ratio between the friction coefficients per unit length of the rod and of the chain segments, and also the network extension, which is characterized by the ratio between the average interjunction distance and the mean-square chain length. Two cases were considered: a chain with the contour length greatly exceeding the rod length and a comparatively short chain. In the case of the short chain, the relaxation times significantly and nonmonotonically were found to depend on the rod length at a given extension. This is explained by a combination of two factors: an increase in the friction of the rod-containing chain fragment and an increase in the statistical elasticity of the chain fragments adjacent to the rod with increasing rod length.