We describe a generalization of the Hybrid Monte Carlo (HMC) algorithm with molecular dynamics (MD) steps that use Nambu’s generalized Hamiltonian dynamics. Time evolution in Nambu mechanics is dictated by multiple Hamiltonian functions, only one of which is required for an accept/reject step. We choose the other Hamiltonian to contain non-local functions of the gauge links, the forces from which enter the MD evolution. In this way, the link variables can be updated with knowledge of the large-distance behavior of the gauge field. We hope that this structure will provide the large-distance communication required to reduce critical slowing down in lattice QCD simulations.