Magnetic susceptibility measurements on conducting polyaniline and polypyrrole nanostructures with different dopant type and doping level as functions of temperature and magnetic field are reported. The susceptibility data cannot be simply described as Curie-like susceptibility at lower temperatures and temperature-independent Pauli-like susceptibility at higher temperatures; some unusual transitions are observed in the temperature dependence of susceptibility, for example, paramagnetic susceptibility decreases gradually with lowering temperature, which suggests the coexistence of polarons and spinless bipolarons and possible formation of bipolarons with changing temperature or doping level. In particular, it is found that the direct current magnetic susceptibilities are strongly dependent on applied magnetic field, dopant type, and doping level.