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Context: High-mass stars and star clusters commonly form within hub-filament systems. Monoceros R2 (hereafter Mon R2), at a distance of 830 pc, harbors one of the closest such systems, making it an excellent target for case studies., Aims: We investigate the morphology, stability and dynamical properties of the Mon R2 hub-filament system., Methods: We employ observations of the 13 CO and C 18 O 1→0 and 2→1 lines obtained with the IRAM-30m telescope. We also use H 2 column density maps derived from Herschel dust emission observations., Results: We identified the filamentary network in Mon R2 with the DisPerSE algorithm and characterized the individual filaments as either main (converging into the hub) or secondary (converging to a main filament) filaments. The main filaments have line masses of 30-100 M ⊙ pc -1 and show signs of fragmentation, while the secondary filaments have line masses of 12-60 M ⊙ pc -1 and show fragmentation only sporadically. In the context of Ostriker's hydrostatic filament model, the main filaments are thermally supercritical. If non-thermal motions are included, most of them are trans-critical. Most of the secondary filaments are roughly transcritical regardless of whether non-thermal motions are included or not. From the morphology and kinematics of the main filaments, we estimate a mass accretion rate of 10 -4 -10 -3 M ⊙ yr -1 into the central hub. The secondary filaments accrete into the main filaments with a rate of 0.1-0.4×10 -4 M ⊙ yr -1 . The main filaments extend into the central hub. Their velocity gradients increase towards the hub, suggesting acceleration of the gas.We estimate that with the observed infall velocity, the mass-doubling time of the hub is ~ 2:5 Myr, ten times larger than the free-fall time, suggesting a dynamically old region. These timescales are comparable with the chemical age of the Hii region. Inside the hub, the main filaments show a ring- or a spiral-like morphology that exhibits rotation and infall motions. One possible explanation for the morphology is that gas is falling into the central cluster following a spiral-like pattern.