A novel continuous low-thrust fuel-efficient model predictive control strategy for multi-satellite formations flying in low earth orbit is presented. State prediction relies on a full nonlinear relative motion model, based on quasi-nonsingular relative orbital elements, including earth oblateness effects and, through state augmentation, differential drag. The optimal control problem is specically designed to incorporate latest theoretical results concerning maneuver optimality in the state-space, yielding to a sensible total delta-V reduction, while assuring feasibility and stability though imposition of a Lyapunov constraint. The controller is particularly suitable for networked architectures since it exploits the predictive strategy and the dynamics knowledge to provide robustness against feedback losses and delays. The Networked MPC is validated through real missions simulation scenarios using a high-fidelity orbital propagator which accounts for high-order geopotential, solar radiation pressure, atmospheric drag and third-body effects.