Multi-Conjugate Adaptive Optics (MCAO) holds the promise of moderate to large adaptively compensated field of view with uniform image quality. This paper is a first effort to analyze the fundamental limitations of such systems, and that are mainly related to the finite number of deformable mirrors and guide stars. We demonstrate that the ultimate limitation is due to the vertical discretization of the correction. This effect becomes more severe quite rapidly with increasing compensated field of view or decreasing wavelength, but does not depend at first order on the telescope aperture. We also discuss limitations associated with the use of laser guide stars and ELT related issues.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.