Propagation of beams in strongly nonlocal nonlinear medium with an elliptically symmetric response is investigated. The result shows that the propagation of beams in this type of medium can be regarded as two-dimensional asynchronous fractional Fourier transform. With this powerful mathematical tool, the analytical solution and the propagation properties of beams can be conveniently obtained. Based on the properties of the two-dimensional asynchronous fractional Fourier transform, the general propagation properties of beams are discussed, the formation conditions of solitons and two-dimensional asynchronous breathers are analyzed, and the law for interaction among solitons and/or breathers is obtained.