This trial is suitable for people that have been diagnosed with an unusual form of melanoma known as neurotropic melanoma. Neurotropic melanoma is characterised by the presence of melanoma cells around nerve sheaths or within nerves. When this type of melanoma is diagnosed on the head or neck region the standard treatment is surgery. This disease may have a high rate of local relapse (recurrence of melanoma in the same area) after surgery. In some hospitals, immediate post-operative radiotherapy is already the standard treatment, but in other hospitals it is not. It is not known for certain whether the benefits of radiotherapy outweigh the risks. The purpose of this trial is to investigate if having radiation therapy soon after surgery is better at preventing the melanoma recurrence than just having surgery alone.