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We discuss the magnetic response of clean Ag coated Nb proximity cylinders in the temperature range 150 µK < T < 9 K. In the mesoscopic temperature regime, the normal metal-superconductor system shows the yet unexplained paramagnetic reentrant effect, discovered some years ago A. Pollini, Phys. Rev. Lett. 65, 1514 (1990)], superimposing on full Meissner screening. The logarithmic slope of the reentrant paramagnetic susceptibility χpara(T ) ∝ exp (−L/ξN ) is limited by the condition ξN = n L, with ξN =hvF /2πkBT , the thermal coherence length and n = 1, 2, 4. At the lowest temperatures, χpara compensates the diamagnetic susceptibility of the whole AgNb structure.PACS numbers: 74.50.+r, 74.80.-g In recent years, there has been extensive experimental and theoretical work in the field of mesoscopic systems, including superconducting structures in proximity with normal metals [1]. In particular, the paramagnetic reentrance phenomenon [2] has received a wide interest, mainly because of being promoted by the recent understanding of the high-temperature diamagnetic response of rather clean normal-metal-superconductor (NS) proximity structures [3] in the context of the quasiclassical Eilenberger theory including elastic scattering [4]. In this Letter, we discuss the very low temperature reentrant behavior of two of the AgNb samples of Ref.[3], covering a larger mesoscopic regime with respect to previous measurements [2].Recently, two Letters [5,6] have addressed the origin of paramagnetic currents in NS systems, which might lead to an understanding of the paramagnetic reentrance phenomenon. The work of Bruder and Imry [5] is based on the presence of non-Andreev-reflecting semiclassical trajectories at the outer surface of a nonsingly connected proximity system (glancing states), which carry predominantly paramagnetic currents. This work has been subject to debate because of the small magnitude [7]. A different, more elaborate approach by Fauchère et al.[6] assumes a net repulsive interaction in the noble metals. The π shift of the order parameter at the NS interface then leads to a paramagnetic instability of Andreev pairs.The first work reflects the cylindrical geometry of our NS system, but it does not address the experimental signatures of the paramagnetic reentrance, namely absolute value of order 1, temperature dependence, nonlinearity, hysteresis, or dissipation [2]. The latter three features might give evidence for a spontaneous magnetization in the samples, as proposed in Ref. [6]. However, the second theoretical approach [6] does not reach beyond qualitative accordance with our experiment.Here we discuss an investigation of the paramagnetic reentrant effect extending to the µK region. By covering five decades in temperature, we have been able to extract the correct temperature dependence of the NS proximity structure below T c . Over a large mesoscopic regime, the cylindrical structure clearly displays different levels of coherence along integer multiples of the wire perimeter L. Unfortunately, neither of th...