[en] The current trend in hadrontherapy is towards high-precision, conformal scanning of tumours with a 'pencil' beam of light ions or protons, delivered by a synchrotron using slow extraction. The particular shape of the slow-extracted beam segment in phase space and the need to vary the beam size in a lattice with rotating optical elements create a special problem for the design of the extraction transfer line and gantry. The design concept presented in this report is based on telescope modules with integer-π phase advances in both transverse planes. The beam size in the plane of the extraction is controlled by altering the phase advance and hence the rotation of the extracted beam segment in phase space. The vertical beam size is controlled by stepping the vertical betatron amplitude function over a range of values and passing the changed beam size from 'hand-to-hand' through the telescope modules to the various treatment rooms. In the example given, a combined phase shifter and 'stepper', at a point close to the synchrotron, controls both of these functions for all treatment rooms in the complex. The modular nature of the design makes it easy to extend the complex