We present some new matrix spectral problems, based on the real special orthogonal Lie algebra so(4,R), and construct corresponding soliton hierarchies bymeans of zero curvature equations associated with these spectral problems. With the aid of symbolic computation by Maple, new soliton hierarchies of Kaup-Newell type, Ablowitz-Kaup-Newell-Segur type andWadati-Konno-Ichikawa type are obtained to illustrate the use of so. (4,R). Copyright (C) 2016 JohnWiley & Sons, Ltd.