Linear surface and waveguide modes with transverse magnetic polarization propagating in a slab of layered superconductor in a uniform dielectric environment are studied theoretically. It is assumed that the superconducting layers are orthogonal to the slab surface and the waves propagate perpendicular to the layers. Dispersion relations are obtained for modes that are symmetric and antisymmetric with respect to the magnetic field. It is shown that the dispersion of these modes is anomalous within a certain range of frequencies and wave numbers. The conditions under which the group velocity of these modes goes to zero are found.