Burgers’ equation, an equation for plane waves of finite amplitude in thermoviscous fluids, is generalized by replacing the thermoviscous termAut’t’(Ais the thermoviscous coefficient,uparticle velocity, andt’retarded time) with an operatorL(u). This operator represents the effect of attenuation and dispersion, even if known only empirically. Specific forms ofL(u) are given for thermoviscous fluids, relaxing fluids, and fluids for which viscous and thermal boundary layers are important. A method for specifyingL(u) when the attenuation and dispersion properties are known only empirically is described. A perturbation solution of the generalized Burgers equation is carried out to third order. An example is discussed for the case α2=2α1, where α1and α2are the small‐signal attenuation coefficients at the fundamental and second‐harmonic frequencies, respectively. The growth/decay curve of the second harmonic component is given both with and without the inclusion of dispersion. Dispersion causes a small reduction of the component. The extension of the generalized Burgers equation to cover nonplanar one‐dimensional waves is given.