Recently, there has been a great effort in studying magnetism in nonmagnetic semiconductors diluted with magnetic impurities due to possible applications in spinbased electronic systems. Moreover, nanoparticles (NP) of inorganic materials including otherwise nonmagnetic oxides such as CeO 2 , Al 2 O 3 , MgO, ZnO, In 2 O 3 and SnO 2 , nitrides, chalcogenides and other functional materials like superconductors and ferroelectrics were shown to be ferromagnetic at room temperature. The magnetism in these NP has been suggested to be intrinsic and originates from cation or anion vacancies at the surfaces of the NP. Very recently, it was reported from both experiments and firstprinciples calculations that typical ferroelectric materials such as BaTiO 3 (BTO) and PbTiO 3 (PTO) become multiferroic when they are prepared at the nanoscale [1 -8]. So, nanocrystalline BTO offers a room-temperature magnetic hysteresis as well as temperature-dependent dielectric constant and a polarization. Multiferroics that exhibit magnetoelectric coupling are widely discussed from quite different context, see [9 -12]. However, apart from a density functional calculation as vacancy-induced magnetism in BTO(001) thin films [13] a well accepted theoretical description of the ferroic properties of nanocrystalline BTO is still missing. In a previous paper [14] the static and dynamic properties of KH 2 PO 4 (KDP)-type and BTO-type ferroelectric NP have been reviewed. Based on that approach we propose a statistical model which reflects the multiferroic properties of BTO-NP. While the spontaneous polarization in a classic ferroelectric material like BTO is expected to diminish when the particle size is reduced [14-16], ferromagnetism cannot occur in bulk material [17]. It is observed experimentally that the multiferroic nature emerges in an intermediate size range of nanocrystalline BTO. Whereas the ferromagnetism is arising from the oxygen vacancies or point defects at the surface of the NP the ferroelectricity is originated from the core of the material [1][2][3].As demonstrated in [14] the Ising model in a transverse field is also appropriate to describe the properties of ferroelectric NP. The Hamiltonian reads e 1 2Since the ferroelectricity in BTO is originated from the off-centering of the Ti ions with respect to the cubic perovskite crystal we assume as the simplest model that there are two positions of the Ti atoms in a double-well potential. These two states are mapped on the S z -component of a pseudo spin-1/2 operator whereas the S x -component Based on a microscopic approach we demonstrate that the unexpected ferromagnetic properties of BaTiO 3 (BTO) or PTO observed recently at room temperature are due to oxygen vacancies at the surface of the nanocrystalline materials. Such vacancies lead to the appearance of Ti 3+ or Ti 2+ ions with nonzero net spin. The resulting different valence states composed of Ti 3+ or Ti 2+ offer a nonzero magnetization which decreases with increasing particle size. The system shows a multiferroic behavior belo...