High-frequency propagation in waveguides or ducts can be formulated in terms of a guided mode or a ray expansion. When the duct is very wide, the excessively large number of modes or rays often necessitates the truncation of the resulting mode or ray series. This paper examines the truncation problem and shows that a hybrid formulation, in terms of a properly chosen number of rays and guided modes, can account for the remainder field in either case. The hybrid field representation has appealing physical content in that a few of the lowest modes account for the collective behavior of rays with many reflections, while a few of the lower-order rays account for the collective behavior of the higher-order guided modes. Other field representations involving rays, modes, a canonical integral, a continuous spectrum, and nearfield perturbation are also examined. Numerical comparisons for a specific example show the utility and range of validity of these alternative representations.