The diffraction of a Gaussian ultrasonic beam in absorbing fluids produces a Gaussian field distribution in the fundamental component. An analytical expression for the second harmonic is derived and it is also a Gaussian function in the quasilinear approximation. Our expressions for the second harmonic are free of the nearfield oscillations characteristic of the radiation from a piston transducer. Calculated results are compared with measurements taken with a Gaussian transducer. Reasonable agreement between theory and experiment is found for both the fundamental and the second harmonic of an initially sinusoidal Gaussian ultrasonic beam in water at 2 MHz. An Appendix is given in which expressions are derived for the first four harmonics of a Gaussian beam. All harmonics are found to obey a Gaussian function. Moreover, the Gaussian coefficient of thenth harmonic is exactlyntimes that of the fundamental component. This means that the width at half maximum changes in proportion to 1/(n)1/2. The phase shift across the beam behaves in a similar manner.