An analysis is presented of a class of leaky-wave antennas based on the slitted asymmetric ridge waveguide which is both easy to manufacture and very flexible in terms of electrical characteristics. The analysis is based on the development of an accurate transverse equivalent network and on the derivation of a dispersion relation which gives the complex longitudinal propagation coefficient in terms of the structural parameters. Both air-filled and dielectric-loaded ridge waveguides are studied. A detailed parametric analysis is carried out showing how the real and imaginary parts of the complex propagation coefficient can be controlled with a good degree of independence from each other. The results presented indicate that the slitted asymmetric ridge waveguide is a promising candidate for millimetre-wave-antenna applications.