Abstract: The authors studied the relationship between basis function neural networks and the reproducing kernel function in this paper. With the condition of that activation function φ (x) ∈C-1, 1ⁿ, it was proved that the basis-function neural networks could be represented by a serious of reproducing kernel functions. Mathematical expressions of reproducing kernel functions were given to the basis-function neural networks. To the general feedforward newral networks, it was also representated by some reproducing kernel functions. Mathematical represeutations of reproducing kernel functions were given to the general feedforword neural networks as a conclusion.