This paper is concerned with the start-up problem in pipeline transportation of gelled waxy crude oil after a period of shutdown. The analysis presented is based on a three-yield-stress model, which has been experimentally verified for waxy crude oil. Three possibilities of the start-up process are discussed according to the applied pressure relative to the complex yielding behaviour of the oil, which is represented by three characteristic yield stresses an elastic-limit, a static and a dynamic yield stress. The physical model of the start-up assumes that the gelled oil is to be displaced by introducing another fluid under constant pump pressure and that the displacing fluid displays time-independent yield stress behaviour. Using rheological property data for a gelled crude oil from the North Sea and a time-dependent Bingham style equation, the flow after a successful start-up is simulated by computing changes in the oil flow rate with time, and the clearing time as function of the applied pressure and characteristics of the displacing fluid. Both laminar and turbulent Rows of the two fluids are considered in the model. The results indicate that the yield stress and the time-dependent rheology of the gelled oil play an important role in determining the oil flow rate after start-up, and that the start-up computer model is highly sensitive to the rheological behaviour of the gelled oil. An appropriate method for measuring the rheological properties of waxy crude oil for this purpose is described. (C)1999 Elsevier Science B.V. All rights reserved.