Neural Networks have recently been a matter of extensive research and popularity. Their application has increased considerably in areas in which we are presented with a large amount of data and we have to identify an underlying pattern. This paper will look at their application to stylometry. We believe that statistical methods of attributing authorship can be coupled effectively with neural networks to produce a very powerful classification tool. We illustrate this with an example of a famous case of disputed authorship, The Federalist Papers. Our method assigns the disputed papers to Madison, a result which is consistent with previous work on the subject.