Shape-memory polymers produced from many natural or synthetic raw polymers are able to undergo a shape transformation after exposure to a specific external stimulus. This feature enables their use in minimal-invasive surgery with a small, compact starting material switching over to a more voluminous structure in the body. The use of biomaterials in modern medicine calls for compatibility tests with cell types, encountering the biomaterial during a short-term or long-term in vivo application. We analysed the cell behaviour of L929 mouse fibroblasts, human mesenchymal stem cells, human mesothelial cells and rat mesothelial cells on a biodegradable shape-memory polymer network to assess its suitability for medical applications. Further, we investigated the differentiation capacity of mesenchymal stem cells into osteoblasts and adipocytes on the polymer and we analysed the influence of the shape-memory effect on adherent cells. The polymer was cytocompatible for all tested cell types, supporting cell viability and proliferation. The differentiation capacity of mesenchymal stem cells was supported by the polymer and shape-memory effect activation did not affect the majority of adherent cells.