An experimental investigation on the transport and dynamics of the optically oriented spins in quantum nanostructures was presented. Their dynamics was explored in dependences of the bias field, the orientation and strength of the magnetic field as well as of the sample temperature. In the exact Voigt configuration, the initial polarization was found to increase with decreasing temperature, while the spin oscillation frequency increased with increasing the strength of the bias, indicating that bias-induced reduction of the exchange coupling between the electron and hole spins was occurred in the quantum structures. It was also found that the deviation from the Voigt configuration is accompanied by an increase in the oscillation frequency and a decrease in the polarization amplitude. The obtained results, however, suggest that the bias-induced breakage of the coupling between the electron and hole spins pays a crucial role in holding the electron spin orientation for a relatively long time, while the hole spin exhibiting fast relaxation.