The oil and gas industry uses dedicated computer models to design their production systems, which typically includes the reservoir, wells, pipelines, and processing facilities (such as separators, compressors, pumps). In these models, the well and the reservoir are often considered as separated systems that communicate with each other through the near wellbore region. The size and geometry of both systems are often completely different yielding distinct spatial and temporal characteristic length scales. Typically, well phenomena are in the order of seconds to hours, whereas reservoir phenomena range between days and years. This motivates the approach to treat both systems separately, as the dynamic response of one system is hardly influenced by the other system. However, there are certain dynamic flow phenomena where the transients have compara- ble time and length scales, such that a coupled simulation approach is necessary. The goal of this project was to extend the Shell single phase well-reservoir simulator to two-phase flow for simulation of well reservoir transients. To achieve this goal, four different steps were identified: a literature study was carried out, a two-phase reservoir model has been developed, an existing well code has been mod- ified to include a two-phase drift-flux model, and the coupling between the well model and the reservoir model has been designed. This research is conducted in the team of Shell Projects & Technology, as part of a master graduation project at the Delft University of Technology. The project has been finalised within a period of 11 months. The two-phase immiscible reservoir equations have been discretised in space using a second-order accurate finite volume method. Second-order time integration was obtained using implicit BDF2 time integration, which is necessary due to the stiff character of the reservoir equations. The well model uses a drift-flux formulation. An existing well code, which is a second-order accurate finite volume method, has been modified in order to be coupled to the reservoir. Again, BDF2 time integration is employed for the temporal discretisation. The coupling has been realised in a monolithic fashion. The coupling with respect to single phase flow has been modified to accommodate the drift-flux model. The coupled simulator showed no difficulties in run- ning simulations with either very small time steps (seconds) or large time steps (years). This stable behaviour is greatly desired, since it enables solving different types of applications with one single simulator. Two different academic cases have been investigated: a production ramp-up (focus on well transients) and a water flooding case (focus on reservoir transients). Based on these cases, the following can be concluded. When considering the dynamics in the well, the transients in the reservoir need to be taken into account. The comparison of the coupling with a dynamic reservoir and an Inflow Performance Curve (IPC) showed that the transient behaviour in the well was calculated incorrectly when an IPC was employed, stressing the need for a coupled simulator. When considering dynamics in the reservoir, the transients in the well have a negligible effect on the dy- namics in the reservoir. The characteristic time scales of the reservoir are generally larger (several orders in magnitude) than the time scales of the well. In this case, the need for a coupled simulator is less evident. The long term goal of Shell is to extend Compas, which is their in-house dynamic multiphase pipeline and well simulator, with a dynamic reservoir model. The two-phase model for the well that is available in Compas is different from the drift flux model used in this study. Shell is particularly interested in simulating liquid loading and in designing intelligent systems, such as smart wells. The coupling through multiple coupling points is essential. Therefore, it is recommended that the reservoir model should be extended to multiple layers. Second, the focus of this study was on development and verification of a dynamic two-phase well-reservoir code. The performance of the code has been tested using academic test cases. However, the real validation of the model has not been considered. It is thus recommended to validate the model using experimental and/or field data.