The constitutive equations for inelastic thixotropic fluids proposed by Moore and Hahn et al. and for antithixotropic fluids by Peter are generalized into an equation of state F = η(λ, D)D and a rate equation dλ/dt = g_D(λ, D) for both thixotropic and antithixotropic fluids. The properties of these equations and restrictions on their functional forms are discussed. It is shown that thixotropy and antithixotropy can be defined by whether (g_D/D)_λ and (dλ/dD)_e are negative or positive.The behaviour of the fluid is discussed in terms of simple shear flow and the relation of such behaviour to laminar shear flow is indicated. The behaviour is obtained by solving the constitutive equations together with D(t). This gives rise to a line in the (F, D, t) space, and not a surface as is generally believed. The Moore model of a thixotropic fluid is discussed quantitatively as an example.The ways by which the constitutive equations can be determined experimentally are described. The ways in which λ can be defined in terms of experimental results are discussed.