A method is developed which permits a two‐fluid analysis of wave propagation in a magnetoplasma‐filled waveguide including the effects of Hall field, current inertia, space charge, unequal electron and ion temperatures, and diffusion. Maxwell's equations and the two‐fluid equations expressed in one‐fluid notation are reduced to a pair of coupled wave equations for the longitudinal components of the electromagnetic field. Approximate solutions are obtained for uncoupled TE and TM modes of propagation in a hydromagnetic waveguide. Included is a discussion of the effects of pressure, resistivity, displacement current, and current inertia on the dispersion relations.