With the widespread of the Model-Driven Development (MDD) and surfing on the success of the Unified Modeling Language (UML), software development is shifting from being code-centric to model-centric. Models become the key artefacts in the software development process. The success of the project relies on the quality of these models. Early detection of errors by debugging and testing these models is manda-tory in order to reduce development cost, ensuring quality and preventing rework at later stages. The fUML standard defines the precise semantics for executing a subset of UML models by defining a virtual machine. The models are then directly executed without transformation. However, the vir-tual machine is defined to execute the model as an atomic action and does not fulfil the requirements for debugging it. We highlight in this paper the limit of the current specifica-tion of fUML (v1.0) and propose an approach for extending the virtual machine with the key functionality that enables debugging of fUML models. A working UML debugger pro-totype has been implemented and the use and evaluation of the approach are made on a case study.