Based on the Snyder-Mitchell model that describes the paraxial beam propagating in strongly nonlocal nonlinear media and by constituting the trial solution with modulating the Gaussian beam by Ince polynomials in elliptic coordinate，the close forms of Ince-Gaussian beams have been accessed. Depending on the power of the beam，the Ince-Gaussian beams can be either a soliton state when the input power is equal to the critical power or a breather state. The Ince-Gaussian beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The profiles of the breather at different propagating distance are numerically obtained and the transitions of a few Ince solitons are given.