An investigation is made of the importance of (n,γ,n,γ,β - ) second-order reaction interferences in reactor neutron activation analysis (NAA), in addition to the commonly considered (n,γ,β - ; n,γ) interferences. The algorithms for the calculation of the interference are derived from the Bateman-Rubinson equation, taking into account the formation of all m- and g-states involved, burn-up effects, and the growth of the interfering radionuclide after irradiation due to a mother-daughter relationship. The following practical cases are examined in detail: 1 3 8 Ba→ 1 4 0 La (detemination of La in presence of excess Ba), 3 9 La→ 1 4 1 Ce (Ce in La), 1 6 4 Dy→ 1 6 6 Ho (Ho in Dy), 1 8 6 W→ 1 8 8 Re (Re in W) and 1 9 2 Os→ 1 9 4 Ir (Ir in Os). A computer search was done for the nuclear data involved in the computation. For 1 3 9 La[(n,γ; n,γ; β - ) + (n,γ; β - ; n,γ)] 1 4 1 Ce, and 1 6 4 Dy[(n,γ; n,γ; β - ) + (n,γ; β - ; n,γ)] 1 6 6 Ho, experimental checks were performed in the Budapest Research Reactor, which confirmed the calculations showing that the (n,γ; n,γ; β - ) interference gives the largest contribution to the apparent concentration of Ce in La and of Ho in Dy, respectively.