Fluids that do not exhibit Newtonian behaviour. That is, the rate of shear is not directly proportional to the shear stress over all values of shear stress. (p. 256) Instead, the viscosity depends on shear stress and/or time. Non-Newtonian fluids are classified as being time-independent, time-dependent, and viscoelastic. They exhibit characteristics where the apparent viscosity either increases as the rate of shear increases, such as polymer melts, paper pulp, wall paper paste, printing inks, tomato purée, mustard, rubber solutions, protein concentrations, and are known as pseudoplastic, or decreases as the rate of shear increases. Examples of the latter are comparatively rare but include TiO₂ suspensions, cornflour/sugar suspensions, cement aggregates, starch solutions, and certain honeys.

With time-dependent fluids, the relation between shear stress and shear rate depends on the time and flow history of the fluid. They can be classified as either thixotropic or antithixotropic (or rheopectic). For thixotropic fluids, the shear stress will decrease with time for a fixed value of shear rate. A simple explanation is that as the liquid is sheared, the structure breaks down. If a cyclic experiment is carried out, a hysteresis loop is formed. Examples include greases, printing inks, jelly, paints, and drilling muds. For antithixotropic (rheopectic) fluids, the shear stress will increase with time for a fixed value of shear rate. Examples include clay suspensions and gypsum suspensions.

Viscoelastic fluids possess the properties of both viscosity and elasticity. Unlike purely viscous fluids where the flow is irreversible, viscoelastic fluids recover part of their deformation. Examples include polymeric solutions, partially hydrolyzed polymer melts such as polyacrylamide, thick soups, crème fraîche, ice cream, and some melted products such as cheese.