Abstract: The basic concept of direction-basis-function neural networks is described. By the method of analyzing the approximation capabilities of affine-basis-function and radial-basis-function neural networks, it is verified that direction-basis-function neural networks can approximate any direction-invariance function defined on a finite set, uniformly approximate any direction-continuum function defined on a unit sphere, and averagely approximate any p-order direction-integral function in the L_p-norm.