  The filiform and the quasi-filiform Lie algebras form a special class of
nilpotent Lie algebras. The aim of this paper is to compute the index and
provide regular vectors of this two class of nilpotent Lie algebras. we
consider the graded filiform Lie algebras $L_{n}$, $Q_{n}$, the $n$-dimensional
filiform Lie algebras for $n$ $<8$, also the graded quasi-filiform Lie algebras
and finally Lie algebras whose nilradical is $Q_{2n}$.
