We report a number of experiments, mainly rheological measurements, examining the yielding behavior of colloidal glasses with hard-sphere interaction plus a short-range attraction. The system is a suspension of nearly hard-sphere colloidal particles and non-adsorbing linear polymer which induces an adjustable depletion attraction between the particles. The pure hard-sphere glass shows a simple yielding process at a strain corresponding to the maximum distortion of the cage of nearest neighbors-the structural arrest length scale. However, the attraction-dominated glasses show a two-step yielding process at different ranges of strain. We suggest that the first step at low yield strain corresponds to the breaking of attractive bonds between particles. The other at larger strain corresponds to the cage breaking process. (C) 2008 The Society of Rheology.