In few types of cancer, genomic abnormalities have been linked to the phenotype and carcinogenesis with a degree of precision. For most cancers, however, this is not the case and the literature provides no clear indication of any logical process. The main difficulties are the great redundancy within the genome and proteome, the vast number of interconnections and the vast number of feedback loops. Such complicated systems can be modelled, but will require highly sophisticated analysis using computational mathematics techniques. Neural networks have been in common use in medical research for the past 20 years. They have been used for classification and for prediction of hazard or failure but are still not widely used for explanation. The binary output can be modified by, for example, adding a Bayesian function to the output stage so that survival probabilities can be given. We looked at the application of probabilistic neural networks in providing prognosis in two types of cancer; laryngeal carcinoma which has a relatively short hazard time and a medium survival rate and ocular melanoma with longer hazard time and higher survival rate. We compared their performance with the more traditional methods and studied their limitations and boundaries.