Passive linear nonreciprocal devices, such as isolators or circulators, require gyrotropic media. If there is a contribution to the dielectric permittivity tensor of odd order in the magnetization, the modes propagate differently in the forward and the backward directions. We investigate dielectric waveguides that are formed by a rib of rectangular cross section on top of a planar structure. The rib or planar structure may consist of layers, each of which may be gyrotropic. We extend the spectral-index method for calculating differences between forward- and backward-propagation constants. A new design for an efficient nonreciprocal phase shifter is proposed.