This trial is being conducted at the Instituto Universitario de Oftalmobiología Aplicada and the University of Valladolidto to investigate the safety and effectiveness of transplanting different donated stem cells in patients with Limbus Insufficiency Syndrome. In this condition, vision is limited due to ulceration and opacity of the cornea. Participants in the trial will be randomly assigned to a treatment group where they will receive donated stem cells from the eye (limbal epithelial stem cells), or a second treatment group where they will receive mesenchymal stem cells collected from donated bone marrow. Participants will be assessed for complications, survival of the grafted cells and changes in vision. The trial is expected to enrol 30 subjects and to complete in February 2014.