The European Space Agency ESA has started the development of the Infrared Space Observatory (ISO), that will be launched in 1993. The TNO Institute of Applied Physics has been contracted for the major part of the optical/mechanical design of one of the 4 scientific instruments of ISO. This instrument, called the Short Wavelength Spectrometer (SWS) will measure stellar spectra in the wavelength range of 2.5 - 45 μm and will operate at a temperature of about 4K. The severe performance requirements together with weight and space limitations made a special instrument design necessary, using an all reflective grating spectrometer configuration with excotic shaped aspherical mirrors. At this moment the Qualification model of the SWS has been assembled and aligned and some optical, thermal and vibration tests have been performed with satisfying results.