The paper concerns about the idea of passive magnetic observer and magneto-mechanical effects (reversible and irreversible) to non-destructive testing and monitoring of critical elements (NDE&SHM). The diagnostic task is regarding as the fast identification of overload elements, which have not broken, cracked or deformed yet (detect 1st and 2nd stage of damage). Theoretical and experimental results from evaluating the early phase of the material fatigue have been presented. Issues have been discussed on two examples (classes of diagnosis task for passive magnetic observer): a) testing object is located only in the EarthÕs magnetic field, b) testing object is located in the EarthÕs magnetic field and low alternating electromagnetic field.