The cross sections for ²³⁸Pu(n,f) reaction for equivalent neutron energy of 13.0–22.0 MeV have been determined by the “surrogate ratio” method by measuring ²³⁵U(⁶Li,df) and ²³²Th(⁶Li,df) transfer induced fission reactions proceeding through the excited fissioning nuclei ²³⁹Pu and ²³⁶U, respectively, and using ²³⁵U(n,f) cross-section data as the reference. Similarly, the cross sections for the ²³⁶Np(n,f) reaction in the equivalent neutron energy range 9.9–22.0 MeV have been determined by the “hybrid surrogate ratio” method via the measurements of ²³⁵U(⁶Li,αf) and ²³⁵U(⁶Li,df) transfer induced fission reactions, using ²³⁸Pu(n,f) cross-section data as the reference. The EMPIRE-3.1 calculations for ²³⁸Pu(n,f) and ²³⁶Np(n,f) cross sections agree well with the present data, however, they are slightly underestimated by the ENDF/B-VII.1 evaluations.