Nature of unusual resonance signals, which can be registered by spectrometers of electron paramagnetic resonance, are studied in different weakly mineralized biological tissues. The experiments are carried out in a three-centimeter range of waves on human and animal (rats) brain tissues and on the organic component of mollusk shells. In these materials the unusual resonance signals, which have unique dynamic characteristics, are registered. Analysis of the characteristics of the anomalous signals shows that the signals are produced by magnetically ordered particles, which have dimensions in nanoscale range. On the basis of experimental data the conclusions are made, that as a result of biomineralization processes in brain tissues both physiological and pathological mineral particles are formed. The supposition is made, that physiological particles play the important role in operation of a brain, and pathological can be a causes of brain diseases.