We have studied the low temperature magnetic properties of one CI and five CM2 chondrites, well characterized in the literature, and of cronstedtite, the Fe end-member of the (Fe,Mg)-serpentine solid solution. Cronstedtite is highly anisotropic and its relaxation properties below ≈10 K suggest a glassy magnetic behavior. Frustration of the magnetic interactions in octahedral layers would account for the observed magnetic freezing, with a possible role of the random distribution of ferric iron in tetrahedral layers. Based on the comparison between powders and crystals characterized by SCXRD and EMPA, we show that grain size and substitution of octahedral Fe by Mg induce changes in the position of the low-Tmagnetic susceptibility peak. A low-Tpeak is also found in each of the CM2 chondrites, but not in the CI chondrite. It is interpreted as the signature of Fe-serpentines, which are considered by most authors to have mostly formed during asteroïdal aqueous alteration events. The low-Tmagnetic properties of the less altered meteorites compare well with those of cronstedtite, and the position of the susceptibility peak varies with the published degree of alteration. By comparing magnetic data on reference cronstedtite, magnetic and published mineralogical data on CM2 chondrites, we suggest that the evolution of the low-Tmagnetic signature of the latter reflects bulk changes in Fe-serpentines' chemical composition, rather than only mixing between Fe-rich and Mg-rich serpentines. This is analogous to previous observations on the changes in Fe incorporation to Mg-serpentines during progressive serpentinization of abyssal peridotites.