  In this paper we investigate the Lie structure of the Lie superalgebra K of
skew elements of a semiprime associative superalgebra A with superinvolution.
We show that if U is a Lie ideal of K, then either there exists an ideal J of A
such that a determined nonzero Lie ideal connected with J is contained in U, or
A is a subdirect sum of A', A'', where the image of U in A' is central, and A''
is a subdirect product of orders in simple superalgebras, each at most
16-dimensional over its center.
