Some popular parametric diffusion processes have been assumed as such underlying diffusion processes. This paper considers an important case where both the drift and volatility functions of the underlying diffusion process are unknown fuctions of the underlying process, and then proposes using two novel testing procedures for the parametric specification of both the drift and diffusion functions. The finite-sample properties of the proposed tests are assessed through using data generated from four popular parametric models. In our implementation, we suggest using a simulated critical value for each case in additiou to the use of an asymptotic critical value. Our detailed studies show that there is little size distortion when using a simulated critical value while the prolmsed tests have some size distortions when using an asymptotic critical value in each case.