We propose a kinetic theory of hard-sphere fluids which systematically generalizes the Enskog equation by taking successively into account binary, ternary,... dynamic correlations in a system close to equilibrium. The first approximation, beyond Enskog, is displayed explicitly; it reproduces most of the results previously established in limiting cases (short-and long-time behavior, low-density expansions) and appears to give a good description of hard-sphere dynamics for all times and all densities. This explicit study will be presented in another publication.