This paper focuses on networked control of multi-unit distributed plants subject to discrete and delayed communication between the local control systems. A modelbased quasi-decentralized networked control structure that enforces closed-loop stability with minimal data transfer, while simultaneously taking into account the different communication delays associated with the transfer of information between the constituent subsystems, is developed. In this structure, each control system includes: (1) a set of predictive models each of which predicts the evolution of the state variables of a given neighboring unit when measurements are unavailable and is updated when communication is restored, and (2) a set of propagation models each of which uses the delayed measurements from a given unit, together with the past values of the estimated local control action, to generate an estimate of the current state which is then used to update the state of the corresponding model. A combined discrete-continuous system formulation of the networked closed-loop plant is developed and analyzed, leading to an explicit characterization of the closed-loop stability properties in terms of the update period, the communication delay sizes, the degree of plant-model mismatch, and the selection of controller design parameters. Finally, the theoretical results are illustrated using a reactor-separator plant example.