  The present paper is devoted to the description of rigid solvable Leibniz
algebras. In particular, we prove that solvable Leibniz algebras under some
conditions on the nilradical are rigid and we describe four-dimensional
solvable Leibniz algebras with three-dimensional rigid nilradical. We show that
the Grunewald-O'Halloran's conjecture "any $n$-dimensional nilpotent Lie
algebra is a degeneration of some algebra of the same dimension" holds for Lie
algebras of dimensions less than six and for Leibniz algebras of dimensions
less than four. The algebra of level one, which is omitted in the 1991
Gorbatsevich's paper, is indicated.
