The field and temperature dependencies of the spin structures in the normal states of La(1.6-x)Nd(0.4)Sr(x)CuO(4) (x = 0.10, 0.12, and 0.15) single crystals have been studied by measuring the magnetoresistance and susceptibility. A negative magnetoresistance appears just below the spin-ordering temperature for the magnetic fields parallel to the CuO(2) plane, which can be attributed to the spin-flop transition of the special spin structure in the normal state of the system. The anisotropic variations of susceptibilities with temperature for all the three specimens can be described in the framework of the crystal-field theory. The well fitted broad peaks of the in-plane susceptibilities χ(ab) for the specimens suggest that the susceptibilities are dominated by Nd(3+), and thus the spin reorientation of Cu(2+) in the CuO(2) plane can not be observed from the study of the susceptibility.