Legged robots such as hexapod platforms are capable of navigating in rough and unstructured terrain. When the terrain model is either known a priori or is observed by on-board sensors, motion planners can be used to give desired motion and stability for the robot. However, unexpected leg disturbances could occur due to inaccuracies of the model or sensors or simply due to the dynamic nature of the terrain. This thesis presents a method based on task-space constraints for real-time stabilisation of hexapod robots which keeps the robot inside defined task-space constraints to recover from unexpected events such as leg slip. A ROS-based control system for hexapod robots is developed and implemented, integrating the presented stabilisation method. The approach is experimentally evaluated using two PhantomX hexapod platforms - one with extended tibia segments which significantly reduces its stability. The results show that the proposed method significantly improves the static stability when unexpected events occur during locomotion.