The linear and nonlinear propagation of a pulsed sound beam generated by a real source in a fluid is considered. The source can be plane or weakly focusing. The investigation is based on a linear and quasilinear solution of the Khokhlov‐Zabolotskaya‐Kuznetsov nonlinear parabolic equation. Analytical and numerical results are presented. The evolution of the pulse as it propagates from the source into the farfield region is investigated for various pulse forms. The special case of a source with distribution exp(−x2/a2)r(t) (x radial distance, t time) is investigated in detail, with emphasis on the role of diffraction and absorption on the self‐demodulation of the pulse. The results are related to the problem of scattering of sound by sound. [Work supported by the IR&D program of ARL:UT and VISTA/STATOIL, Norway.]