  We introduce in this paper the contractions $\mathfrak{G}_c$ of $n$-Lie (or
Filippov) algebras $\mathfrak{G}$ and show that they have a semidirect
structure as their $n=2$ Lie algebra counterparts. As an example, we compute
the non-trivial contractions of the simple $A_{n+1}$ Filippov algebras. By
using the \.In\"on\"u-Wigner and the generalized Weimar-Woods contractions of
ordinary Lie algebras, we compare (in the $\mathfrak{G}=A_{n+1}$ simple case)
the Lie algebras Lie$\,\mathfrak{G}_c$ (the Lie algebra of inner endomorphisms
of $\mathfrak{G}_c$) with certain contractions
$(\mathrm{Lie}\,\mathfrak{G})_{IW}$ and $(\mathrm{Lie}\,\mathfrak{G})_{W-W}$ of
the Lie algebra Lie$\,\mathfrak{G}$ associated with $\mathfrak{G}$.
