We have studied the relaxation and transport properties of a ferrofluid in an elongational flow. These properties are influenced by the bistable nature of the potential energy. Bistability comes from the irrotational character of the flow together with the symmetry of the dipoles. Additionally, the presence of a constant magnetic field destroys the symmetry of the potential energy magnetizing the system. We have shown that at a moderate temperature, compared to the height of the energy barrier, the viscosity decreases with respect to the value it would have if the potential were stable. This phenomenon is known as the ''negative viscosity'' effect. Thermal motion induces jumps of the magnetic moment between the two stable states of the system leading to the aforementioned lowered dissipation effect. (C) 1997 American Institute of Physics. [S0021-9606(97)52146-5].