Nonlinear feedback shift registers (NFSRs) are used in many stream ciphers as their main building blocks. In particular, Galois NFSRs with terminal bits are used in typical stream ciphers Grain and Trivium. Seven types of Galois NFSRs have been found equivalent to Fibonacci ones, among which three types are particular cases of another type of lower triangular Galois NFSRs. This paper continues the research of equivalence between Galois NFSRs and Fibonacci ones. It first enumerates the Galois NFSRs with terminal bits that are equivalent to a Fibonacci NFSR. It then discloses n-stage (n−2)-terminal-bit Galois NFSRs equivalent to Fibonacci ones, must be lower triangular Galois NFSRs. Finally, it presents two new types of Galois NFSRs that are equivalent to Fibonacci NFSRs. Some examples show that, compared to a Fibonacci NFSR, its equivalent Galois NFSR from our new types may decrease the area and increase the throughput of the circuits implementing feedback functions. •Two NFSRs are said to be equivalent if their sets of output sequences are equal.•The Galois NFSRs with terminal bits equivalent to a given Fibonacci NFSR are counted.•n-stage (n−2)-terminal-bit Galois NFSRs equivalent to n-stage Fibonacci ones are lower triangular Galois NFSRs.•Two new types of Galois NFSRs equivalent to Fibonacci NFSRs are given.•Both new types may decrease the area and increase the throughput compared to their equivalent Fibonacci NFSRs.