A theory is constructed for the nonequilibrium statistical mechanics of a many-particle system, including effects of multiparticle correlations. The particular system studied is a dense monatomic fluid, whose atoms interact by pairwise central forces. The nonequilibrium fluid possesses coupled position and momentum correlations, of which the two-particle correlations are treated explicitly, while three- and more-particle correlations are included in a mean-field approximation. A truncated gradient expansion is applied, representing the condition that the one- and two-particle probability densities vary by a relatively small amount under translation through a distance not larger than the correlation length. New concepts which are used in the theoretical construction include the following: a localized nonequilibrium potential of mean force; a nonequilibrium h function and the corresponding h currents; and interaction integrals, which are the counterpart of Boltzmann's collision integral, and which are based on effective two-particle interactions that conserve particle number, momentum, and a statistically appropriate energy. The resulting theory consists of two coupled evolution equations, one for the one-particle probability density, and one for the two-particle correlation function. The evolution equations satisfy the continuum equations for conservation of particles, of momentum, and of energy; the evolution equations also satisfy an h theorem, whose sourcemore » function is a Lyapunov functional, and whose equilibrium solution gives the correct equilibrium values for the one-particle probability density and the two-particle correlation function. The simplified theory that results from neglecting two-particle momentum correlations is also presented.« less