In this work, we study cooperation between UMTS and GSM systems. The aim is to find the best Joint Radio Resource Management (JRRM) strategies that achieve lowest blocking rates. We first present analytical models for capacity in GERAN and UTRAN. We then consider different strategies of Joint Radio Resource Management (JRRM) with or without inter-system (vertical) handovers and show how to calculate the steady-state probabilities and the performance measures (blocking probabilities, loads). Our numerical results compare the different JRRM strategies and point out the advantages and drawbacks for each of them. We show that the best performance is obtained when authorising vertical handovers. However, a simple strategy without vertical handover may, in some cases, achieve comparable performance with less signaling overhead.