We describe a method for multiresolution deformation of closed planar curves that keeps the enclosed area constant. We use a wavelet based multiresolution representation of the curves which are represented by a finite number of control points at each level of resolution. A deformation can then be applied to the curve by modifying one or more control points at any level of resolution. This process is generally known as multiresolution editing to which we add the constraint of constant area. A multiresolution representation for the area moment is also developed. We make sure that all computations are fast and that the deformations can be performed interactively. Diverse types of deformation are discussed.