The impulse theory of flow has been extended to include the rotational motion of the particles of the minority component of certain types of suspension which exhibit non-Newtonian flow behaviour. Some physical considerations are discussed for the flow of a suspension of identical rigid spheres dispersed in a continuous medium exhibiting Newtonian flow behaviour. Steady translational motion produces a steady state distribution of single spheres and multiparticle aggregates, consisting of two or more spheres, which are generated by shear induced collisions amongst the various species of particle. The present discussion is, however, limited to an ideal system consisting of single spheres and aggregates containing only two individual spheres, a multi-link bond being formed between colliding spheres. The two-particle aggregates are approximated to rigid ellipsoids, the rotational and translational motion of the aggregates and the associated hydrodynamic drag forces being considered in relation to the particle-mobility approximation. By specifying the way in which the bond formed between colliding spheres behaves under tension, an expression for the associated impulse has been developed which in turn yields the rheological equation of state. Two regions of flow are distinguished; with increasing flow rate the strength of the bond increases, ultimately reaching saturation at a particular flow rate. For a saturated bond the rheological equation of state is formally similar to that of an ideal Bingham plastic. An experimental technique has been developed which involves measurement of the whole of the transient flow behaviour of the fluids. The measurements yield the shear stress-rate of flow characteristics corresponding to both the initial and final rheological states of the fluids which exhibit thixotropic flow behaviour. Some experimental results are presented for a non-thixotropic fluid and for two fluids which exhibit thixotropic flow behaviour, the measurements being obtained with a coaxial cylinder viscometer. The rheological equations of state, derived by way of the impulse theory of flow, correlate favourably the shear stress-rate of flow measurements for all three fluids.