We prove the convergence of vortex blob methods to classical weak solutions for the twodimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size h does not exceed the smoothing blob size E, i.e., h/~ 5 C. 0 1995 John Wiley & Sons, Inc.