The reaction kinetics for the selective oxidation of n-butane (n-C-4) to maleic anhydride (MAN) over delta-VOPO4, and gamma-VOPO4, catalysts were investigated by a transient response method using the Temporal Analysis of Products(R) (TAP) reactor system. These catalyst phases are contained in selective mixed-phase vanadium-phosphorus oxide (VPO) catalysts for n-C-4 to MAN processes that are based upon multi-tubular fixed-beds, fluidized-beds, or circulating-solids reactors. In the latter reactor type, the catalyst is exposed to alternating zones of hydrocarbon-rich and oxygen-rich reaction gases so the reactor operation can be classified as a type of forced unsteady-state process. Previous kinetic models for n-C-4 oxidation to MAN that are based upon steady-state experiments with oxygen-rich feeds are not directly applicable to this operating mode. TAP reactor step response experiments where n-C-4 and O-2 are cycled over 380-420 degrees C and atmospheric pressure were used to generate transient responses for n-C-4, O-2, CO2, and MAN. It is shown that a kinetic model that combines surface kinetics and solid-state diffusion of oxygen in the lattice is able to predict the transient response data for oxidation and reduction of the VOPO4 catalysts over a reasonable range of reaction temperature and inlet mole fractions of the reactants.