  In this paper we establish some basic properties of superderivations of Lie
superalgebras. Under certain conditions, for solvable Lie superalgebras with
given nilradicals, we give estimates for upper bounds to dimensions of
complementary subspaces to the nilradicals. Moreover, under these conditions we
describe the solvable Lie superalgebras of maximal rank. Namely, we prove that
an arbitrary solvable Lie superalgebra of maximal rank is isomorphic to the
maximal solvable extension of nilradical of maximal rank.
