This paper reports the results of an experimental and theoretical study to investigate the transient response of the granular flow through a laboratory scale inclined rotating cylinder to large step changes in one of three variables: (i) mass feed rate, (ii) rotation speed or (iii) axis inclination. Experimental measurements are reported for a range of operating conditions, sizes of step and a number of cylinder geometries. A mechanistic model for the transient response is derived based on a published steady state model. The dynamic model parameters are the cylinder radius, length, discharge dam height, axis inclination and rotation speed, the granular feed rate, and the bulk density and dynamic angle of repose of the granular material. The model has no adjustable parameters, making it useful for scale-up. The model takes the form of a non-linear partial differential equation, equivalent to a one dimensional unsteady diffusion equation with variable coefficients, and solution has been obtained numerically. Good agreement is found between the model and experiment both in the range of cases considered in the current study, and also for published experimental work, for which the cylinder size and granular material properties differ substantially from those of this work.