Rheological data are presented for shear flows of concentrated dispersions of acicular ferromagnetic particles; such dispersions are widely used in the manufacture of data storage materials. In steady shear flow these dispersions are strongly shear thinning. Upon the inception of shear flow, they show stress overshoots for both the shear stress and the primary normal stress difference. The data can be rationalized in terms of a temporary junction network, resulting from the strong magnetic interactions between the particles, if the network consists of relatively weak magnetic links connecting strongly bound flocs of particles. Application of a shear deformation results in disruption of the initially sample spanning network. The overshoot in the shear stress occurs when the flocs become arranged in the shear planes. The overshoot in the primary normal stress difference occurs as a result of deformation of the strongly bound flocs. (C) 2004 The Society of Rheology.