In this paper, we study the nonparametric estimation of first and second infinitesimal moments by using the local linear method of the underlying scalar diffusion model. The special attention is paid to the asymmetric kernels instead of standard kernel smoothing. We focus on the use of asymmetric kernels when the diffusion process lives on a support with one or two boundaries. We establish the pointwise consistency and asymptotic normality of the proposed estimators under the condition of recurrence and stationarity.