  F-Lie algebras are natural generalisations of Lie algebras (F=1) and Lie
superalgebras (F=2). We give finite dimensional examples of F-Lie algebras
obtained by an inductive process from Lie algebras and Lie superalgebras.
Matrix realizations of the $F-$Lie algebras constructed in this way from
osp(2|m) are given. We obtain a non-trivial extension of the Poincar\'e algebra
by an In\"on\"u-Wigner contraction of a certain $F-$Lie algebras with $F>2$.
