The magnetic properties of the upper Cretaceous red-limestones from the Montsec thrust sheet in the Pyrenees reveal an unusual arrangement of the unblocking temperatures and coercivities of the magnetic mineral phases, which leads to an apparently single-component remanence being isolated on thermal demagnetization. That this is an artefact of the almost complete overlap of the blocking temperature spectra of the two real components, can be deduced from alternating field and thermal demagnetization of a composite isothermal remanent magnetization (IRM). When two IRM components are imparted to the sample, at right angles to each other and each affecting grains with different coercivities, thermal demagnetizations of the composite IRM does not isolate the components but alternating field demagnetization does, illustrating the superiority of the latter treatment in this case. ¿American Geophysical Union 1991