Each of the two Gemini telescopes will be instrumented with the Gemini Multi-Object Spectrograph (GMOS), a general purpose optical spectrograph mounted at one of the Cassegrain foci. Two GMOS are currently being designed and built by a team of scientists and engineers in Canada and in the UK. A stringent flexure specification is imposed on these instruments by the scientific requirement to measure velocity to high precision, 2 km/s at R equals 5,000 with 0.5 arcsec slits. This implies a basic stability specification of 3.125 micrometer/hour at the detector focal plane. The GMOS design has met this specification by using a combination of stiff structure (where flexure is minimized); Serrurier trusses (where the flexure is controlled); precision mechanisms (where mechanical hysteresis and error are minimized) and, finally, an open-loop active correction system at the detector focal plane (where the CCD is translated to counteract any residual flexure). Once the GMOS design was conceptualized and its component groups were identified, the design team divided the basic stability specification into allowable contribution from each group. The final division was weighted according to the degree of design difficulty, based on inputs from the engineers. An error budget was developed and maintained to ensure that GMOS would meet its overall flexure specification by controlling the contribution from each component. The error budget approach will be described and discussed in the paper. We will also look at examples from the GMOS design with reference to calculations, analyses, FEA and actual measurements from prototype components.