Though mathematical morphology can process the binary and grayscale image successfully, this theory can not extend to the color image directly. In color space, a vector represents a pixel, so in order to compare vectors, vectorial orderings must be defined first. In this paper, an adaptive lexicographical ordering is proposed. This approach takes advantage of the vectorial processing of the classical lexicographical ordering, but it can arrange the components’ rank adaptively. In other words, this approach can select the first, second and third component automatically. First, a generalization of an adaptive lexicographical ordering is introduced, and the results of this approach’s erosion, dilation, opening and closing are offered. Comparative application results on color noise reduction and edge detection are also provided.