In nonnested hypothesis testing, J test suggested by Davidson and MacKinnon (1981) and JA test suggested by Fisher and McAleer (1981) are two common tests used to evaluate hypotheses. In this thesis, we first give the necessary background for J and JA tests in nonnested hypothesis testing and the literature survey on these issues. We then compare the performances of J and JA tests with Predictive Residual Sum of Squares method. Monte Carlo experiments are carried out to compare these tests in testing Quadratic versus Leontieff models and also Linear versus Log-Linear models, where we find that Predictive Residual Sum of Squares method has superiority over the other tests mentioned in terms of power. In the end, a real case study testing different consumption function theories for 1987-1995 period in Turkey is presented.