Anomalous axial propagation has been theoretically shown to be possible in a dielectric helicoidal bianisotropic medium (HBM) with local uniaxiality, just like a thin-film HBM (TFHBM). A necessary condition is that the medium be highly dissipative. The anomalous axially propagating fields do not have the ordinary space-harmonic structure; instead, the amplitudes of two of the four axial propagation modes vary linearly along the axis.