It has been observed experimentally that bubbly layers generated by breaking waves form nearly exponential waveguides near ocean surfaces and that noise propagation in such waveguides occurs in distinct frequency bands [D. M. Farmer and S. Vagle, J. Acoust. Soc. Am.86, 1897 (1989)]. It was conjectured that the well‐defined frequency bands are due to the normal mode propagation of sound. Motivated by the experimental observations, a theory is presented to investigate the normal mode propagation in exponential waveguides, by analogy with the optical waveguides formed by diffusion [Z. Ye, Appl. Phys. Lett.65, 3173 (1994)]. The theoretical results compare favorably with the experimental data. In addition, we show that a waveguide with an exponential sound speed profile has great mathematical convenience in that it has simple characteristic equations which can be solved in a closed form. The number of normal modes, which is shown to correspond to the number of discrete acoustic bands, can be determined by waveguide parameters through a simple equation. The results are useful for solving inverse problems associated with exponential waveguides. The present exponential sound speed profile is also compared to the inverse square profile that has been studied extensively in the past. ©1995 American Institute of Physics.