The direct search optimization method of Luus and Jaakola (LJ) and the Gauss-Newton (GN) method are employed to solve four parameter optimization problems for chemical and biochemical processes described by ordinary differential equation models. A comparison of the solution methods was thus carried out. It was found that the impact of initial guess values is minimal on the optimal parameters and the optimum. Gauss-Newton, however, was found to be sensitive to the initial guess. Moreover, GN encountered convergence problems which were alleviated by the use of the Marquardt-Levenberg approach.