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The author proposes a two-dimensional generalization of Constantin-Lax-Majda model.Some results about singular solutions are given.This model might be the first step toward the singular solutions of the Euler equations.Along the same line(vorticity for-mulation),the author presents some further model equations.He possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes e-quations.Some discussions on the possible connection between turbulence and the singular solutions of the Navier-Stokes equations are made.