The ferroelectric and magnetic behaviour of multiferroic BiFeO₃ nanoparticles has been studied using piezoresponse force microscopy (PFM), Mössbauer spectroscopy and SQUID magnetometry. The results of the PFM studies indicate a decay of the spontaneous polarization with decreasing particle size. Nevertheless, particles with diameter ∼50 nm still manifest ferroelectric behaviour. At the same time these particles are weakly ferromagnetic. The Mössbauer spectroscopy studies prove that the weak ferromagnetic state is due to non-compensated surface spins rather than distortions of the cycloidal spin structure characteristic for bulk BiFeO₃.