  It is well-known that all saturated formations of finite soluble groups are
locally defined and, except for the trivial formation, have many different
local definitions. I show that for Lie and Leibniz algebras over a field of
characteristic 0, the formations of all nilpotent algebras and of all soluble
algebras are the only locally defined formations and that the latter has many
local definitions. Over a field of non-zero characteristic, a saturated
formation of soluble Lie algebras has at most one local definition but a
locally defined saturated formation of soluble Leibniz algebras other than that
of nilpotent algebras has more than one local definition.
