By analysis for a series of subspaces and subalgebras in the ultradistribution algebra, a concept of the layer of an ultradistribution is introduced. Any ultradistribution on a certain layer can be expanded not only as a linear superposition in the ordinary sense by the basis elements on this layer, but also a pseudo-linear superposition by the non-total basis elements on the lower layers. A study is made on the physical applications for the two kinds of expansions of ultradistribution.