This work takes aim at presenting a generic real-time simulation framework for marine power plants with weak power grids, containing transient functionalities such as starting and stopping of arbitrary generators, and phase synchronization. The generator models used in the power plant are hybrid causality models, meaning that they have the ability to switch between causality orientations, between voltage and current. These models facilitate real-time simulations as long as they are solved properly, as will be discussed in this article. Much is devoted to numerical stability, model robustness and power plant control, e.g. rms voltage control, engine speed control, active-and reactive power sharing control and phase synchronization control. Some focus is also given to overall power plant control structure. A case study of a marine power plant including two generators and a fluctuating-and noisy power consumption is presented and analysed, and illustrates the advantages of the proposed framework as well as giving a good foundation for future works.