Abstract The interaction between two sound fields of different frequencies propagating in different directions is investigated and a scattered pressure at the sum and difference frequencies is shown (theoretically) to exist outside the volume of interaction. The results of Ingard and Pridmore-Brown, who considered the interaction of two fully collimated sound beams intersecting at right angles, is extended to the case of non-collimated beams to show that the scattered pressure is somewhat less than the value they predicted. Also the work of Westervelt, who claims that no scattered pressure should exist outside the interaction region, is extended to show that scattered pressure fields at the intermodulation frequencies exist just outside the interaction region. A relative agreement is, therefore, brought between the two conflicting results. An experimental investigation is also included. No scattered pressure outside the interaction region is reported. This result is not entirely unexpected since the theoretical value of the maximum scattered pressure is just above the noise level.