In this paper, a novel way is proposed to investigate the transformation between Galois nonlinear feedback shift registers (NLFSRs) and Fibonacci NLFSRs. First, the Galois NLFSRs and Fibonacci NLFSRs are regarded as two Boolean networks (BNs), and the corresponding algebraic equations are obtained based on semi-tensor product (STP) of matrices. Then, the definition of absolute equivalence is given to investigate the transformation between these two kinds of NLFSRs. Furthermore, some interesting results are presented to achieve the transformation. Finally, an example is provided to illustrate the effectiveness of obtained results. (C) 2018 Elsevier Ltd. All rights reserved.