  We show that in the class of solvable Lie algebras there exist algebras which
admit local derivations which are not ordinary derivation and also algebras for
which every local derivation is a derivation. We found necessary and sufficient
conditions under which any local derivation of solvable Lie algebras with
abelian nilradical and one-dimensional complementary space is a derivation.
Moreover, we prove that every local derivation on a finite-dimensional solvable
Lie algebra with model nilradical and maximal dimension of complementary space
is a derivation.
