This research investigated unsteady events such as stall inception, stall-cell development, and surge. Stall is characterized by a decrease in overall pressure rise and non-axisymmetric through-flow. Compressor stall can lead to surge which is characterized by quasi-axisymmetric fluctuations in mass flow and pressure. An expanded Greitzer model is presented to predict the stall and surge characteristics of a two-volume, two-throttle compression system. The current work provides a method to experimentally determine the time for a stall cell to fully develop after stall inception. This value is required for the model. Experimental stall and surge characteristics are compared to the predicted characteristics. Individual values of the upstream and downstream B parameter had the largest impact on the system dynamics for the compression system studied. The ending post-stall throttling point was found to influence the system dynamics in cases where the upstream and downstream value of B where close to the critical values. Unsteady measurements of the flow field around the compressor rotor are examined. During the stall inception process, initial disturbances were found within the rotor passage near the tip region. As the stall cell develops, blade lift and pressure ratio decrease within the stall cell and increase ahead of the stall cell. The stall inception event and stall-cell development for stable rotating stall and surge were found to be nearly identical. A stalled compressor rotor can be considered to contain three main regions: stalled passages, recovering passages, and over-pressured passages. Over-pressured passages exhibit turning and pressure rise greater than pre-stall values.