It is well established that helium formed in stainless steel by various (n,α) processes has a pronounced effect on its mechanical and dimensional properties. The anomalous production of helium in nickel-based alloys is known to take place via the two-step process: 58Ni(n,γ)59Ni(n,α)56Fe. For thermal neutrons, the 59Ni(n,α)56Fe cross section used to calculate the helium production differs strongly from the value obtained by the direct measurements of this cross section. In this Note, this discrepancy is discussed, and a value of 12.5 ± 1 b based on direct measurements is recommended for future calculations. For fast neutrons, the contribution due to the two-step process has been ignored in the past. It is demonstrated that this contribution is substantial, and it gains in importance as the neutron fluence increases. It is further shown that the usual practice to relate helium production data to thermal- and fast-neutron fluence is inadequate. The details of the neutron spectrum and the cross section are necessary to reliably predict the helium production rate.