Transversely pumped dye-doped slab waveguides are investigated. A set of coupled-rate equations for the excited-state population and for the amplified spontaneous emission (ASE) power, at all wavelengths, is presented. The equations are solved numerically for the steady-state case. The results describe the dependence of ASE output power on pumping power, the spectral narrowing process, and the effect of waveguiding. The theoretical calculations are compared with the results of experiments, and good agreement is found.