It is impossible for a zoom lens to image perfectly throughout its zoom range. That is, regardless of how complex a zoom system is made, there are necessarily residual aberrations. The principles of Hamiltonian optics can be used to determine the smallest level of such residual aberrations for a specific set of design requirements: zoom range, field of view, speed, etc. The best imagery that can be achieved by a zoom system, in the geometric limit, is referred to as the fundamental limit. The nature of the residual aberrations at the fundamental limit is investigated for a particular class of zoom system. It is found that the coefficients of the wave aberration function associated with each of the lens groups is not unique at the fundamental limit. As an example, the fundamental limit for a particular zoom system is determined, and the possibility of using this information in design is discussed.