In this paper,the propagation properties of a paraxial elliptic Gaussian beam in strongly nonlocal nonlinear media are discussed.We obtain a set of evolution equations for the param eters of the elliptic Gaussian beam,and also their exact analytical solutions.When the beam propagates in the media,the beam widths in the two trasverse directions oscillate generally along a propagation direction.What ever an intial power is,the elliptic Gaussian beam will evolve into the circular ly symmetrical Gaussian beam,then evolve back to the elliptic Gaussian beam agai n,but with the change of its major axis into the minor axis.This process is peri odic.For a certern initial power,the beam width in one trasverse direction can k eep constant,which is an optical soliton state,while the width in the other tran sverse direction vibrates.
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