  We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n)
inspired by Kostant's cohomological interpretation of the classical theorem. We
show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type
super identity if p, q are non zero and conjecture that neither can any other
classical simple Lie superalgebra with the exception of osp(1,2n).
