Transient stability studies are primarily concerned with the generator response of ac power systems and use only steady state type equations to model HVdc converter terminals. These equations are adequate for small disturbances at the converter terminals but cannot accurately represent a converters behaviour during, and through its recovery of, a significant transient disturbance. A detailed three phase electromagnetic analysis is necessary to describe the converters correct behaviour. This thesis describes an accurate and effective hybrid method combining these two types of studies, for analyzing dynamically fast devices such as HVdc converters within ac power systems. Firstly, conventional techniques are reviewed for both a transient stability analysis of power systems and for an electromagnetic transient analysis of HVdc converters. This review deals in particular with the two programs that constitute the hybrid developed in this thesis. Various techniques are then examined to efficiently and accurately pass the dynamic effects of an HVdc link to an ac system stability study, and the dynamic effects of an ac system to a detailed HVdc link study. An optimal solution is derived to maximise the inherent advantages of a hybrid. Finally, the hybrid is applied to a test system and its effectiveness in performing its task is shown.