An introduction to nucleosynthesis, the creation of the elements in the big bang, in interstellar matter and in stars is given. The two--step process $^4$He(2n,$gamma$)$^6$He and the reverse photodisintegration $^6$He($gamma$,2n)$^4$He involving the halo nucleus $^6$He could be of importance in the $alpha$--process in type--II supernovae. The reaction rates for the above processes are calculated using three--body methods and show an enhancement of more than three orders of magnitude compared to the previous adopted value. Direct--capture calculations give similar values for the above reaction rates. Therefore, this method was also used to calculate the reaction rates of the two--step processes $^6$He(2n,$gamma$)$^8$He and $^9$Li(2n,$gamma$)$^{11}$Li and the reverse photodisintegration of $^8$He and $^{11}$Li that could be also of importance in the $alpha$-process.
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