This volume contains the post-proceedings of the Fourteenth and the Fifteenth International Workshops on Graph Computation Models (GCM 2023 and 2024). The workshops took place in Leicester, UK on 18th July 2023 and Enschede, the Netherlands on 9th July 2024, in each case as part of STAF (Software Technologies: Applications and Foundations). Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modeling in science, engineering, and beyond, including computer science, biology, and business process modeling. Graph computation models constitute a class of very high-level models where graphs are first-class citizens. The aim of the International GCM Workshop series is to bring together researchers interested in all aspects of computation models based on graphs and graph transformation. It promotes the cross-fertilizing exchange of ideas and experiences among senior and young researchers from the different communities interested in the foundations, applications, and implementations of graph computation models and related areas.